How to disassemble a pop-up trip lever drain in tub?
My pop-up sink drain had a similar problem.  I finally figured out that the top screws off the stem like the cap of a mushroom.  I had to show it who's boss and that I meant business, but it finally unscrewed and I was able to clean the drain.

You may also find that if you take the handle out, the spring is clogged with hair (that used to happen to me as well.)