You say "I subleased my apartment" meaning the subtenant signed something between himself and you? If so, what?
He declined to sublease the apartment based upon what? For example, does he claim you misrepresented something about the unit, that it was infested with rodents or cockroaches, or something else that might justify his change of heart? Or is this a "no reason" / "I found a cheaper place"-type of thing?
Yes, you should be trying to mitigate your damages by finding a different subtenant.

