Yes,
There is not much holding the axle in usually just an E clip or a gear retainer
If one side can spin freely then the other will not drive much at all
The other end generally has a spline which can also strip.
So it is out with he tranny and pull it apart.
They are not very complicated and the hardest bit is cleaning them enough to split the case .
For you the important thing will be to take lots of photos so you can remember where everything went.
On the tranny itself should be some stickers with the makers name, and the model number of the transmission plus a bar code.
IF you can find it and post it people here can pull up service information & parts availibility