“Can cancer spread after surgery?”

Cancer can always spread, but this is not typically due to have surgery. The goal to surgery is to remove the cancer completely so that it won't spread. However, if the tumor cannot be completely removed or is growing into surrounding structures, the likelihood of the tumor coming back is increased. Similarly, if the tumor has spread to lymph nodes, then there is a much higher risk that it can recur or spread to other organs. There are many factors that cause a tumor to spread, but surgery is a tried and true treatment that allows for cure of many tumors. Once the tumor is removed, there is always a chance that it could come back and spread, but this is usually due to other factors - size of tumor, grade of the tumor cells (how aggressive the cells look under the microscope), Stage of the tumor, etc.
Working with you cancer team will allow a comprehensive plan to be put into place along with continued follow up after surgery.

Yes, it can happen. But this really depends on the type of cancer you have. And also depends on whether it had spread to the lymph nodes or not.