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I am clearly disheartened by the Editor's behaviour:

I sent a manuscript for peer review nearly three months back to an Elsevier Journal with impact factor 0.625 in Mathematics.

I inquired about the status of my manuscript after 1.5 months since it was still showing "With Editor " status.

The Editor said review process is on and a decision can be obtained after 1 month.

After 1 month I again inquired about its status to which the Editor said that the report can be obtained in a few days.

But after that nearly 3 weeks have passed but I did not get the report.
I have mailed the Editor 2 times and the Associate Editor 1 time but no one replied.

The status is still showing With Editor.

Why is the Editor behaving this way with me? I am waiting anxiously for my report as it matters a lot to me.

Are they avoiding my mails intentionally by not replying?

What is their aim? Do they want me to withdraw my paper? Should I withdraw my paper because the Editor is behaving so badly with me?

NOTE: Also if the Editor is busy why is the Associate Editor not replying?

The situation is sub-optimal, but not as bad as you seem to think. Remember that being an editor to a scientific journal, even one published by Elsevier, is often a volunteer job. Moreover, the editors have no control over how long the reviewers take to review your article. (which reminds me...) So what they gave you was only a guess. If the guess was wrong, then that happens. What seems to worry you the most was the status of your paper. I would not worry about that. Sometimes editors use these function to track submission and sometimes they don't. If they do, then the status is probably fairly accurate, if they don't then it means nothing.

My suggestion is to think about publishing your article until you submit the article. After that you just forget about it (don't look at the journal website, don't think about it), because there is nothing you can do. Instead, focus on writing the next article. Only when you get your rejection letter, you start thinking about it again, and improve the paper and submit it to the next journal.

The typical time to get a decision from a math journal is about 10 months. To put this in perspective, I was recently asked to referee a long math paper and the editor said I can take four months. As such, it is a bit unusual to contact the journal after less than two months.

However, don't wait forever. I once waited a year to contact the editor, and was told the paper had been accepted 11 months earlier. A mishap in the mailroom, it seems. (This was decades ago.) I generally contact the editor at about the 5 month mark. I have had too many papers get lots when there is a change in the editorial board, or whatnot.

So I say: if an editor is behaving badly, you can consider withdrawl. Just be prepared to give the new journal a year. In your case, the editor is not behaving badly. At worst, the editor meant "I expect a report from a referee in a few days" and wrote "you will see a decision in a few days."

By the way, my first paper took about two years to be accepted. I assume that had a small negative effect on my career. One reason to write smaller papers is that it increases the odds that one is accepted before the next job-hunt or grant-submission season.

By the way, I am speaking about pure math. I only have one applied math paper so am not sure how things work for applied math journals.

I inquired about the status of my manuscript after 1.5 months since it
was still showing "With Editor " status.

I've found that six months tends to be about the average length of time before a paper in pure mathematics receives a referee's report, though it might take a few months less if the paper is especially short or non-technical, and a few months longer if the paper is on the technical side or is hard to find a referee for. Even when dealing with journals that I know for a fact explicitly tell their referees to get them a report within a few months (since I also have refereed for them) I've found that it's pretty rare to get a report before six or so months have gone by.

You've said that you inquired about the status of your manuscript after going 1.5 months without a report. I'm sad to have to be the one to break the news to you that, at least in the areas of math I'm familiar with, there's an excellent chance that the referee hasn't printed out your paper to start reading it yet.

Why is the Editor behaving this way with me? I am waiting anxiously
for my report as it matters a lot to me.

Remember, the editor and referee aren't being paid by the journal. So if they have to choose between spending time with your paper and spending time prepping their classes, writing a lecture, meeting with their students, etc, your paper is going to get pushed aside.

Also, and I think this gets forgotten too often, the editor and referees are people. Perhaps the past couple of months have been very stressful for them. Perhaps they have something major happening in their personal lives. Perhaps they're even sick in the hospital. (I once had an editor pass away while handling a paper of mine.)

The point of the above isn't that you shouldn't expect editors and referees to take your paper seriously. It's that you should remember that they aren't your personal employees. Sending a polite inquiry about the status of your paper every few months is totally acceptable, though you should probably wait until at least 3 or 4 months have gone by first. Sending near daily emails is not acceptable and is, I think, extremely unlikely to wind up with a positive result for you.

Finally, you should keep in mind that it's definitely possible that the referee is having trouble finding a referee for the paper. (You should take the online status updates like "With an Editor", "Under review," etc with a grain of salt.) Finding a good referee for a paper can take quite a bit of time if the paper is technical or in a niche area.

Are they avoiding my mails intentionally by not replying?

If you've been sending an abnormal number of emails then perhaps they are intentionally not responding. But it's also possible that they simply don't have anything to say. Perhaps after they received your initial email they reminded the referee about the paper and asked when they might expect a report. If you email them again two weeks later then there probably isn't much that they can even do. After all, if they start sending frequent harassing emails to the referee then they'll likely be told either (1) that the referee won't be able to complete the report in the timeline that the editor wants and that perhaps they should get someone else, and / or (2) that the referee won't want to referee any future papers for the paper. Either way it's a loss for the editor.

What is their aim? Do they want me to withdraw my paper? Should I
withdraw my paper because the Editor is behaving so badly with me?

I know that it's extremely important to you that your paper be published in a reasonable amount of time, but as I said above, you should keep in mind that most pure math papers take 6-ish months to get refereed, and many mathematicians have had papers that took years to get refereed.

Mu suggestion is that you try to remember that the editors and referees involved with your paper are almost certainly doing so voluntarily as a service to the mathematical community, and while they are committed to doing a good job, have their own full time jobs to worry about.

You can withdraw your paper, but this means you have to start the process all over again. And of course there's also the possibility that you simply get assigned the same referee.