Biopsies.
Some wide cancer excisions, depending upon the location. I personally would like it if dermatologists could also do sentinel nodes and stuff, but I'm weird that way.
Derms can do something called a Mohs fellowship after residency. Mohs microsurgery a special technique used to assure clear skin cancer margins while taking the least amount of tissue possible. The problem is that not all dermatologists will be able to close complex Mohs excisions, and the pt will end up going to plastics for closure of the defect. I'd like to see dermatologists get more aggressive learning how to use various flaps for closure, etc.
Some dermatologists will do skin grafts.
Some derms take things up a notch and do lipo and blephs, etc.
Dermatologists also get to play with lasers, which is fun and rewarding.
I'm one of those crazy people who thinks the term "derm surgeon" doesn't have to be an oxymoron. I'm sure there'll be plenty of folks (esp. the plastics people) who will disagree vehemently.