Save Game Locations
From Battletech Modding Wiki
Depending on which store you brought the game from your Save games can be in different locations.For Steam the location is:
\Steam\userdata\ USER_ID \637090\*Note for steam users, you should be able to right click, properties and find it, if any one does kjnow the location please add.
For GoG the location is:
c:\users/<user>/appdata/local/gog.com/<game id>.GoG Galaxy Users:
c:\users/<user>/appdata/local/gog.com/galaxy/applications/50593543263669699.The game ID may change.