My mechanic is saying that the differential in the trans is not turning the axles but it shifts fine?

 

Does it make any noise while youre in gear, release the clutch as if you want to move from a dead stop? The shifting components and differential are totally unrelated, and one may work without the other. Put the car in gear while car is off(apply e-brake), lift the car in the front and rotate the tires by hand to see what the other tire does. If One tire spins and the other one doesnt while its in gear, there is something wrong with the differential(assuming you have a working clutch).

 

BY THE WAY, also assuming BOTH axles are snapped into the differential as they should. When an axle retaining ring becomes worn, it will pop the axle out and cause similar symptoms. hope it helps.

Oscar