How to express the following idea in a natural way?
Someone wants to do something which is beyond his means in order to flaunt his success and wealth. For example, Mike, a poor guy, is not affordable a diamond. However, to capture his girlfriend's heart, he applies for loan from the bank to buy the expensive diamond. Therefore, that makes him heavily in debt. Is the expressions below acceptable?
He does something beyond his means in order to be impressive.
"to be impressive" suggests that he is impressive. To see him is to be impressed by him, by his size, or wealth, or personality, but the point is that he is impressive.
I believe you mean "to impress." That is, his actions are designed to impress someone; he is not necessarily impressive otherwise, but is simply contriving to impress.
Therefore, I would suggest something more like, "He spent beyond his means to impress her."
"Spent beyond his means" can be further improved by simpy saying more directly "he went into debt": i.e., "He went into debt to impress her."
On a side note, your sentence "For example, Mike, a poor guy, is not affordable a diamond" is awkward at best. I'm sure you meant to say, "... cannot afford a diamond."