I can guarantee that your lender would be upset. I suspect your mortgage contract has a prohibition on such without lender permission and even if it didn't it most likely has a due on sale clause that will be triggered with the deeding necessary to divide the property.
Notwithstanding all that, dividing the lost doesn't change the security interest which would apply to all the divided properties. It wouldn't be much different than deeding the whole property away. The person getting it would still. have a property encumbered by the.previous mortgage.
If the mortgage doesn't get paid, the bank will foreclose on the entire property. No sane person would take ownership of a property like that (and certainly no other bank would finance a property still subject to such a security interest).
And as Welke points out, "splitting" a lot may not be a trivial task based on local zoning and other ordinances. I had an amusing "I told you so" incident with our developer. He decided that it would be more desirable to merge two lots together (figured a larger lot would sell better). I told him that was a stupid thing to do. If someone wanted a big lot they could buy both and put them together themselves, but if he did it, he'd lose the possibility of splitting them out and selling them separately. Sure enough, when the big lot didn't sell, he tried to split them again and the county refused saying that it didn't meet the requirements for subdivision.