I assume you are at the net, and what's coming your way is a ball with heavy slice, and pretty much just skimming over the net. You can punch it to a good depth (which you know how to do), but you're looking for the alternative of just dropping it short (and possibly also angled) over the net.
If so, then the shot you're trying to play is more of a stop volley than a drop volley. To do so, you have to take a lot of pace off the incoming ball, by holding the racketface to the ball at contact point but then cushioning the impact (so the racketface moves a little bit backwards, rather than punching forward), i.e., you start at contact point, and then there's some "give". Therefore, the key is that at contact point the ball meets the sweetspot (rather than closer to the frame), and that you start the cushioning at contact - hence, a lot of watching the ball into the strings, and good timing.
As for the normal "punch" on a ball carrying slice, you have to realise that the ball will both "float" a bit more than expected and also will be fractionally "checking/slower" than expected because of the underspin (as compared with a ball coming with topspin). So the start of your cushioning will be both fractionally higher (contact point) and also fractionally later.