What would you do with a 75 by 31.5 inch basement doorway?

First, check whether those are the opening measurements or the size of the old door. A slab needs clearance inside the jamb, so the leaf will be smaller than the opening. Also check the swing and the hinge and latch locations before ordering anything.

If it’s an interior door, ask a local door or lumber shop about a slab made to your measurements. Trimming a standard slab by several inches can expose the core or leave too little solid material for hardware, depending on its construction. Check the maker’s trimming limits before cutting.

Building the door and jamb yourself can work, but it’s more than cutting a panel to size. You’ll need a stable, square frame, suitable material for the location, and solid places to attach the hinges and latch. Measure the opening in several spots first, since older openings aren’t always square.

If you go this way, make a simple drawing with the finished door size and clearances, then choose the materials and hardware around that. It can be a reasonable project if you’re comfortable with accurate cuts. For an exterior door, use materials and construction intended to handle exposure.

Before making a custom door, see whether the framing can be adjusted to fit a standard prehung unit. That may be simpler if there’s room to alter the opening. If not, a custom slab from a door shop is another option worth pricing, rather than assuming a custom installation is the only way to get one.

I’d be cautious about cutting a lot off a hollow-core door. The edges can lose their structure, and the cut itself may leave the door unusable. A barn-style slider is only a fit if the room has the space and you don’t need the usual sealed, hinged-door setup.