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Recently our GM has given the party an item that could easily break the game for the rest of the campaign. We were given a Sap of Healing that deals 1d6 damage and after successfully hitting a target heals the wielder 1d6 HP as well. There are no limits on HP healed, nor any conditions on how the item heals (such as no healing provided from undead or constructs). This would mean, with a little bit of cheesing, our characters will always be at max health between encounters.

As a player, I believe an item like this is tremendously overpowered and shouldn't exist. However, I don't think anyone else in the game feels the same. The GM intended this to be a 'gag item' and I don't think he realizes how this will affect the game. I've not talked to the other players yet but when the weapon was introduced, none seemed to think the weapon was overpowered. None of the characters have any disapprobation towards the weapon.

No one in the party has laid claim to the item yet, and it is currently in possession of my character, the wizard, since I was the only one who could determine its properties. I had made a spellcraft check of 37, and determined the weapon was not curse or hiding any other properties. I've talked with the GM and suggested that it be modified to be a "Vampiric" weapon or to put some sort of constraints on the amount of healing it provided so it doesn't trivialize the game.

Am I overestimating the power of this weapon? If not, what can I do to prevent this weapon from breaking the game?

The item was originally a sap and dealt nonlethal damage, but could be used to deal lethal damage with a -4 roll. The healing is not a drain ability, so a character striking themselves with the weapon would still benefit from the heal. Due to magical healing recovering both lethal and nonlethal damage, the average roll of 1d6 (3.5) for heal would cancel out the average nonlethal damage (3.5) but also heal an average of 3.5 lethal damage. Thus we could restore an average of 35 HP per minute using this item.

The GM later modified the item so that it could only do lethal damage, but there's still nothing to stop a character from gathering chickens or raising zombies for us to use as cannon fodder to sacrifice to the sap.

tl;dr

My GM introduced an overpowered item to the party and how can I prevent this item from breaking the game?

Out-of-combat Healing Does Not Break The Game

This is not broken at all, because most high-level parties will buy a wand of cure light wounds which generates the same effect. It's not free but it's very cheap.

You've told us your wizard got a Spellcraft check of 37, so your group can almost certainly afford a wand of cure light wounds. Your group should always be at max hit points between encounters anyway.

Seriously, go buy a wand now. Buy two of them, so you'll have a spare in case the first runs out.

Summary

This is has been called the Bag of Rats Problem and there are a number of ways to deal with it. But, at the end of the day, you probably don't need to worry about it. If your DM probably didn't intend to give you "unlimited free healing" they will likely jump in if/when you exploit this item. If/when that happens, or if you get sick of the item before the rest of your group, you can suggest one of these solutions:

Option 1: Use as intended

This requires you to play your characters as if they are characters. While it is technically feasible for you to carry around a bag of rats and relentlessly murder them between encounters...it's a pretty weird thing to do. Most people wouldn't do it unless they're rather strange.

But...maybe your party is full of orcs and dragonborn and you're already a bunch of weirdos. What's a bag of rats to you? In that case...

Option 2: Figure out the logistics

This is a great trick whenever a party I'm DMing for wants to do something. I say "OK, but how, exactly, are you doing this?"

Are you guys literally going to carry around a bag of rats? That disgusting. You'll probably get bitten every time you stick your hand in. The whole party is going to be at higher risk of food poisoning. Then there's the NPCs: People in town won't let you in their stores. The guards might not even let you in the city gates!

A bag of chickens might be less weird, but chickens are bigger and also pretty loud. Goodbye stealth checks!

However you get these "free kills", there can be consequences. If you're summoning zombies over and over again, that's got to take spell slots. Even if it doesn't, you might draw the ire of some dedicated doers-of-good who don't take kindly to all the weird necromancy....

Option 3: Add some rules

If you're still worried, perhaps the sap can have a certain number of charges (maybe 10 with a recharge of 1d10+3/day). Or set a size limit for the creatures that get summoned (at least small size?).