Whether only a monument by the time of this photo, apparently at some point the cadets did have a functional 8-inch siege mortar (and Gatling guns!) at their disposal for military drills. (ref: "Adventures in Martial Education" 1993 Duane Ernest Miller, Berlin Green Press, Lansing, Michigan, page 112).
The original Academy opened in 1877 and didn't close until 1908 so the pose happened somewhere in there. It appears the property was placed on the National Register of Historic Places in 1982 with the Orchard Lake (SE Michigan) Schools Historic District, if it still exists.
btw the ref. also indicates the cadets trained with ".45 caliber Springfield Rifles," whatever those were.