On most models (mechanical locking ones) you DON'T want to engage it with one wheel spinning and the other stalled, you want to let the wheels stop and hold the pedal down until you're clear. It's fine to engage with the wheels moving roughly the same speed.
Assuming it's mechanical (not hydraulic clutch pack) it engages pins inside the differential to lock it so both wheels turn together, once engaged it will hold until the wheels equalize torque and release on it's own, like how you can shift out of gear when there's no load on the transmission but not when the engine is working or being worked.