For how long is the recover process of getting a plantars wart surgically removed?

Depends. It depends where on the bottom of the foot it is and how deep it is. Generally about 2 weeks.
2-4 weeks. If the wart is large and a deep area is removed it will take more like 4-6 weeks for complete healing to take place. Most small areas will heal within a few weeks and patients can get back to normal activity.