You have to do something about it because the horn may grow right into his eye or his skull - not nice. Have a feel of the horn with your bare hand wrapped around it and see if you can feel where the horn turns from cool to warm closer to the head. Practice on the other horn. If the bit which is too close to the eye is the cool part, then it is OK to remove it. If the warm part, ie where there is an arterial blood supply, is approaching his eye then you have a problem.
Speak to your vet again. If you have a vehicle you can take the tup in, take him down to the vet rather than calling the vet out - much cheaper and he/she will have all the equipment to hand.
The vet should do the procedure under sedation if the sensitive part is involved, and use cautery to stop the bleeding after removing as much of the horn as needed, applying heat to each artery and arteriole, plus prolonged pressure to help stop the bleeding. They may also have the same kind of blood stopping dressing they use in dentistry, plus a pressure dressing over the cut end.
It sounds though as if your vet is unsure of how to proceed, or the problem was not as severe as it is now, when he/she saw it before. Whatever is done, you will need to keep a close eye on further growth. A he's a pet I assume you will not be thinking of using him for breeding. If you are then don't as the tendency for horns to grow in is an hereditary trait.