What it does is

I believe the original sentence is elliptical, in that the infinitive sign 'to' has been eliminated. I have a negative feeling about your second sentence.

There are others here who can better answer the question, so let's wait for them.

Debpriya De "What it does is [that] it makes us laugh ?"
Is the second sentence grammatically correct ?

I think it's grammatical enough, but it may sound unidiomatic or bad to native ears. (Read Philip's reply.)

Philip is right about the first sentence: make is a plain/bare infinitive.

CB

@CB, Why do you say that the second sentence is grammatical ?
"that it makes us laugh" is like a fact or a condition, and we cannot "do" a fact or a condition.

Debpriya De@CB, Why do you say that the second sentence is grammatical ?

Because I can't find anything ungrammatical in it. A that clause after What it does is may be a little unusual but I know of no grammatical rule that prevents it. A Google search for "what is does is that it" gives more than 70,000 hits, most of them written by native speaker

Debpriya De "What it does is make us laugh ?"
Sometimes people say such sentences as "What it does is it makes us laugh ?"
Is the second sentence grammatically correct ?

What it does