Our kitchen is extremely outdated and to save money, we are going to paint our hand crafted, wood cabinets. However, they are extremely long and I only have 12.5" from the countertop to the bottom of the wall cabinet. I would like to cut off the bottom portion of the cabinet. Is this possible?
While this might seem like a dumb question, are you absolutely sure your kitchen wall cabinets can't be raised? You mention that your cabinets were custom built, so it's very possible that the previous owners wanted extremely tall units. But perhaps they wanted their standard height cabinets lower to provide more access to the cabinets' contents without the use of a step-stool. If that is the case, there may be a bulkhead constructed to close off the space between the top of the cabinets and the kitchen ceiling.
You should be able to tell by just looking at the top of the cabinets. If they extend all the way to the ceiling, then you don't have a bulkhead. However, if there is a vertical section of sheetrock or another wall covering between the cabinets and the ceiling, then the kitchen has a framed bulkhead. Most of the time bulkheads can be removed during a kitchen remodel so that the cabinets may be raised, but you might have a few issues that have to be addressed.
HVAC and electrical contractors often use bulkheads as an easy avenue for running their ducts and wires in the kitchen. The wires should be able to be moved up into the ceiling framing without too much trouble, but depending on their size and the direction the framing runs, ductwork could pose a small problem. If you have this situation, I recommend having an HVAC contractor look at the current arrangement. There's a good chance they should be able to figure out a solution.
Hopefully you have a bulkhead in your kitchen because if the cabinets extend all the way to the ceiling, shortening them could be a major project. Without seeing the actual cabinets, I would assume that each frame would need to be adjusted and the rear and side panels trimmed. This would involve removing each unit and would require the services of a very experienced trim carpenter. There is no doubt in my mind that in trying to take the frames apart some components would need to be replaced.
I'm not sure what type of cabinet doors you have, but if they're not flush panels, there's a good chance you'll have to purchase a new door for each shortened cabinet. While almost anything is possible for a skilled cabinetmaker, it would be very difficult to adjust a recessed or raised panel door to match the new cabinet opening and have it look attractive.
If you don't have a bulkhead, purchasing new kitchen cabinets might be less expensive than trying to modify your existing units -- they'll probably look much better as well.