Is It Possible to Remove Mole Near Tear Duct?

I would highly recommend that you see a board certified facial plastic surgeon or an oculoplastic surgeon for an evaluation and possible treatment.

If the tear duct is damaged, a possibility is tearing unless a further procedure is done to correct it. Most oculoplastic surgeons work well near the tear duct. I am sure the surgeon you are seeing would use their judgement and not take a chance if it is out of their range. Tearing from tear duct damage can need a glass tube to be placed in the eye socket to drain the tears which doesn't work as well as good old mother nature.

As a dermatologist, I frequently remove moles near the tear duct. Certainly one has to be careful, and thus a specialist such as a dermatologist or plastic surgeon are both quite capable of doing this safely and with great results.