Can any relative clauses be reduced?

For this sentence:

I am a student who has little money.

Can I rewrite it as:

I am a student having little money.

Do they make a same sense?

If not, when should we use the reduced relative clause instead of the relative clause?

Answer

Yes you can use both constructions and they mean the same.

Obviously you have your main clause and your relative clause.

I am a student who has little money.

As deadrat has correctly identified your second sentence contains a participial clause

having little money

It's a non-finite clause using a present participle. Thus, it's called a participial clause.

However, that's just half the truth because the clause still acts as a relative clause. It's mostly overlooked as even the Wikipedia entry states and not always described as such as you will see below.

Some nonfinite clauses, including infinitive and participial clauses, may also function as relative clauses. These include:

present participle clauses having an unvoiced zero subject argument that takes an antecedent to the argument: The man Ø sitting on the bank was fishing. (These clauses are the least likely to be recognized as relative clauses.)

The posted excerpt also contains the answer to your question.

You can find further explanation and examples over here and here.

A participial relative clause is a clause which resembles a relative clause but which contains a participle instead of a finite verb.

So to conclude, it's real tricky and with English having no central language authority the naming of such edge cases is always disputed. The point remains, you are a student and you don't have a lot of money, in both your sentences.