After hair transplant, will it cause any problems if I shave my head with a razor?

Generally, shaving the head with a razor too soon after a hair transplant can negatively affect the total yield. For this reason, it is a good idea to wait until the scalp is healed (at least 10 days after surgery) and the crusts are no longer present.

If you shave your head after a hair transplant surgery, it would seem to defeat the purpose of having a hair transplant surgery in the first place.

Typically after 2 weeks all of the grafts are well healed and the scabs have long since fallen.  At this point, hair cuts and short cropping of the hair can take place.
You will still want to be careful if you are using a razor at this point, as you may still cause some irritation to the area of the transplanted hair.  Depending on how quickly you heal, you can do this sort of close shave any time after 3-4 weeks.

Generally it's recommended to wait a month before doing so unless your doctor has told you otherwise. You can trim your hair earlier if you'd like to clean up your look in the meantime! Good luck with your results.

If all of the crust are off and you are at least 3 weeks after your hair transplant, then a razor cut should be ok

You should wait until 4-6 weeks to shave your scalp. You could however trim your hair as close as required.