by losses that he aggressively employs to avoid paying taxes

Yes.

He uses his past losses to legally avoid paying taxes.

Past losses can be used to offset current income if you have a good tax lawyer.

So for example if you lost a million dollars two years ago, but you earned a million dollars this year, you could claim that your income this year is zero.

I think the idea is that you are not gaining "new" income but only making back what you previously lost.

I'm guessing the question is about the use of the word "employs"?

If that's the case, the word here doesn't pertain to people who work for him, or the process/act of employing someone.

In this sentence, you can substitute the word "uses" or "makes use of".