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"What would you say, if I asked if you were blind, and you were allowed to respond verbally?"

so that:

Blind person raises hand for yes. Non-disabled person raises hand for no. Mute person would not be able to respond verbally, and raises no hands. You only said that it must have those three answers - not that it must be a standard yes/no question.

Firstly,

Determine the relative position of the mute person with respect to the person who is neither mute nor blind (without loss of generality, suppose the mute person is 1 metre to the left of the non-mute non-blind person).

Then ask

"Is the one mute person in the room 1 metre to your left?


where the bold section can be replaced by the relative position.

Result

The mute person will immediately raise their left hand. The non-mute non-blind person, determining that this must be the mute person, will then raise their right hand. The blind person will raise no hand.

Alternatively

You could find a discrepancy between the mute person and the non-mute non-blind person.


Suppose for example the non-mute non-blind person was taller than the mute person. Then you could ask "Are you taller than the one mute person in the room?"

The mute person would again raise their left hand immediately, the non-mute non-blind person, will then raise their right hand. The blind person will raise no hand.

Original Incorrect Answer: Before question was edited.

You could

Write on a piece of paper "Are you mute?" and show it to them.


The question does not state that asking be done verbally.

Result

The blind person won't raise any hand, the mute person will raise their right hand and the other person will raise their left hand

The question would be

Raise my hand, and then ask, If you are mute lie, am I raising my hand?

Explanation

Blind won't raise his hand. Mute will raise his left and the third will raise his right.

I think this could be an answer:

Can you pronounce this word? (pointing to some written word)

- The non-impaired: YES (right hand up)
- The mute: NO (left hand up)
- The blind: No answer (No hand up due to lack of information: What word?)

You say:

One of you is blind, another is mute and the other is normal. If I was to add either $0$ or $1$ to the number of people with disabilities you can see, would you have a number greater than $1$?

And then:

The blind person sees $0$, the mute can see $1$, the normal $2$.

The sum results in: $0+0lor1le1,1+0lor1ge1,2+0lor1gt1$

So 'No, Don't Know (the mute now has either $1$ or $2$), Yes' indicate 'Blind, Mute, Normal' respectively.

You could ask (not really a question, but could probably be worded that way).

"When I raise my index finger, please raise the hand that corresponds to whether you are mute."

This means that

The blind person will not answer (cannot see visual cue), the mute should raise their right hand, and the other person should raise their left hand.

Old (incorrect answer)

"What would you vocalize if I were to ask you 'Am I holding up three fingers'?", but actually only hold up two fingers for them to see.

This would mean that...

The blind man person would stay silent, since he cannot see and verify the number of fingers held up. The one with no disability should answer "No", since he can see they are wrong. The mute person should stay silent as well, since they cannot normally vocalize either "Yes" or "No".

I would ask:

Could you honestly say my eyes are blue? (or some other truthful visual fact about yourself)

That way:

The blind person can't know whether the fact is true or not, so will raise no hands. The mute person can't speak so would raise their left hand. The neither blind nor mute person would be able to know and speak truthfully so would raise their right hand.

And I would know who's who.