If one has access to conduct experiment in a Machine Lab, s/he may please verify possibly following two things:
1. Without appreciable change in speed, torque and consequently output reduces to 1/ SQRT (3) or 57.735%.
2. If total supply is switched off, it may not start when switched on; hence requiring some other means. Once started it will however, continue to run, of course with reduced output as stated above.
In best case, if the mechanical load is light, the motor will continue to rotate.
In worst case, the motor will stop running. If there is no adequat overcurrent protection to trip, the motor will end up burning.
Anyway, don't try to start again the motor with one phase disconnected. The motor will not rotate but only vibrate, before overcurrent protection trip or motor burning.