What doctor removes foot corns?

Podiatrist. You can always reach out to podiatrist for such conditions. Although a dermatologist does have the right tool for corn removal; however, very unlikely that a dermatologist would even bother.
Foot Specialist. Many patients believe they have a foot corn or callus when it's actually a wart or a different soft tissue lesion. Most Podiatrists will be able to determine the exact cause and the proper treatment of all the above! Best wishes!
Short or long term.. There are different meanings to the phrase "remove corns". If you mean by shaving for temporary relief, but most likely doomed to return, often times worse. Or is removing a corn directed more to the permanent removal, involving surgical intervention. Podiatrists usually perform both tasks.