I only have plans for the 8" mortar so I will discuss making one of them. A 10" is substantially (about 50%) larger.
The basic dimensions for an 8" M1861 siege mortar are 16" barrel diameter, 22" overall length (actually plus the elevation notches, maybe another 1/2" or so), 22.9" across the trunnion ends and an extra 3" for the lifting lug. The trunnion centers are 10" from the muzzle. The trunnions are 10" in diameter and 3.25" wide, the rimbases are 11.5" in diameter and the diagonal across the trunnion corners is 24.9".
If I were to cast one, the only machining I would do on it is (1) drill the bore and touch hole, (2) drill the lifting lug, (3) face the muzzle, and (4) machine the trunnions. All of that could be done on a large vertical mill with a heavy duty rotary table. Drilling the bore on a lathe would require at least a 25" swing to clear the corners of the trunnions.
The greatest difficulty would be holding the casting to drill and face because there is no cylindrical portion on the rear to hold. I might make the casting with integral lugs for holding which would be ground off after the machining processes requiring them were completed.
Actually, since I am more interested in launching bowling balls than 8" or 10" shell, I would fabricate one from thick-wall tubing and round stock and not worry too much about the deviations from the actual 1861 pattern.