If it was actually a quote, they can't amend it without advising you of the projected increase and asking if you'd like to proceed. If they didn't give you that advice, I'd suggest you had a good chance of just paying the original quote and refusing to pay the extra they added without warning.
However, you say later on in your posts that it was an estimate, not a quote. As you accepted it as an estimate, then sadly you're probably legally obliged to pay, irrespective of how much extra they added.
I really think you could have grounds to take this to their governing body though - they've not been clear about their costs if it's just an estimate and that to me is poor practice. Vets know we'll do anything for our pets and this smacks of "taking advantage" to me.
Obviously unexpected circumstances can arise even with the best planned surgery, but I'd say an "estimate" was pretty much a blank cheque for the vet.
Can they actually justify the tripling of the cost? How? I'd want an itemised bill, and full explanation of the extra costs etc, laid in black and white in front of me on paper to discuss with them before I'd even consider paying.
I'd certainly not be using their services again. It feels very deceitful and the trust would be gone forever.