I suspect the holder of the mortgage will definitely be involved since they (apparently?) hold title to the land. The bank will get the money (or at least the amount the bank consider the 1/2 acres is worth).

The bank will be VERY involved.

The mortgage is on the entire 4 acres. If the bank gives consent, your son may be able to survey and subdivide the property with the county. However, the bank may wish to have the entire remaining mortgage balance from the proceeds of the sale. Your son may be able to negotiate a new mortgage on his remaining acres.

The bank will not release title to the land until it has been paid.

It is the bank's 4 acres until the mortgage is paid off.

He needs to talk to the mortgage holder and find out if they will allow it, then do what they tell him to do.

If he just takes the money from the neighbor and tries to hand over a title it's not going to work.

I talked with a mortgage specialist from the bank and received an answer: the bank will appraise the 1/2 acre to be subdivided and also appraise the remaining 3-1/2 acres. If the property appraises for more than the amount of the mortgage, the bank would not necessarily require the proceeds from the sale of the 1/2 acre. If less, they would.