Okay I bought a door from Habitat Restore. The men there told me what I was buying was a solid oak wood door. I wanted solid wood door because house has odd sized door (31 & a quarters inch wide by 72). Figured w/ solid wood door would be no problem cutting it down to size needed. After husband went to cut door to width it was found to have chipboard core. Not sure if door is usable now...it seems it would have been better to get hollow core door from YouTube videos watched as all you have to do is replace wood piece inside. Cant hardly find anything on cutting chipboard core door. Is it salvageable w/ it no longer having solid wood piece on side? Can only return for in store credit & doubt they will take after being cut.
I'd suggest you chuck the door. Chipboard won't hold hinge screws well, nor will it make an attractive surface for the strike side.
If you were desperate to use this door, you could cut a channel in the chipboard edge and insert/glue a 2" piece of solid wood. Getting a really clean surface inside the channel would be hard.
At 31-1/4, you're pretty close to a 32" door, so you shouldn't have a hard time finding something appropriate.
For what it's worth, many in the door industry call this kind of door "solid core". I'd give volunteers at the Restore a little leeway for getting the description wrong.
Your question is how to make the door you bought work, but it really should be how to install a new door. Might I suggest that you abandon the plan to fit a door into the existing door opening (jamb)? Since the existing door opening is not a standard size, you would need to either have a door custom made, or cut one down, and hope you can make it work.
It is likely that the existing opening is no longer square. Fitting a door into that opening will present a challenge. Even if you could cut it to fit the opening, chances are that the door couldn't be closed properly. There would probably be ugly gaps on the top or bottom as well.
The best solution would probably be to get a brand new pre-hung door. There are 2 standard widths available which are very close to the existing opening. You could go with either a 30", or a 32" door. Big box home stores typically carry solid wood doors in those standard sizes. If they don't have one in stock, they can usually order one in any size, or design that you would like. As long as they don't consider it a custom made door, you can get them for a reasonable price.
If you are trying to make the new door match another door in the house, you could have one custom made. Just be sure to give detailed measurements, and pictures of the original one. You would want to measure the height, width, thickness, as well as the size of all of the panels, and stiles and rails. Stiles are the vertical members of the door, and the rails are the horizontal ones.
You may be able to reuse the existing trim with the new door. You will just need to be very careful when removing it. If the existing trim will not work, you may need to have it custom made to match the original woodwork.