In survival analysis, can the last follow up date be with a different specialty I'm interested in collecting the date follow up for patients with cancer of the uterus. it's retrospective chart review. Can the date of last follow up include visits to different specialties or it has to do with the same specialty (to answer the question whether disease recurrence occurred or not)?

The answer depends on what you are using for the events of interest.
In survival analysis, death is often taken to be an event (overall survival). In that case, being alive at any follow up indicates that the event hadn't occurred by that date. You can use the date of last follow up to get a lower limit to overall survival duration (a right-censored survival time), regardless of the observing clinician. So you should be transcribing dates of all follow up visits, for overall survival at least.
If cancer recurrence is the event, then you have to apply your understanding of the subject matter, as John Madden indicated in a comment.
Evaluating time to cancer recurrence is tricky enough in the best of studies. The cancer was presumably present in clinically undetectable form since the original therapy, so "recurrence" is just when the remaining cancer grew large enough to become detectable. That depends on the methods used to detect recurrence. A gynecologic oncologist would presumably look harder and use more sophisticated methods to evaluate recurrence in a patient who had previous uterine cancer. A dermatologist treating the same patient would assume that the oncologist was evaluating the patient for cancer recurrence, and not pursue the cancer issue beyond making sure there weren't any overt signs of trouble.
To resolve those issues, discuss with your colleagues on the project and decide among yourselves how you should proceed. In the process, think about how you would justify your decision to a skeptical audience.
The timing of cancer recurrence has an additional, statistical, problem arising from the intervals between follow-up visits. If a patient returns for follow up every 6 months, has no recurrence at one visit, but has recurrence at the next visit, what do you choose for the time of recurrence? It happened sometime during that 6-month window, but you don't know when. That is best handled as an "interval-censored" time to recurrence. In practice, the recurrence date is nevertheless often taken to be the date of the follow-up visit where the recurrence was first seen. That imposes a bias toward longer times to recurrence.
