shutting off power to circuit after a short time from an alarm clock
I'm starting to feel like an old engineer suggesting these so frequently recently, but you can use a 555 timer in monostable operation. When triggered (by the alarm), these maintain high signal for a set amount of time and do not accept additional triggers during that time. 

You might need to make this as two stages if the original alarm signal continues to set one off when triggered (like if the alarm signal is the driving signal for a buzzer). The way that works is one is high for the length of the buzzer, accepting no other triggers, the output of the first stage triggers the second, which is monostable for the length of the vibration motor. Basically this allows both to be triggered on the same edge, but the shorter duration one can not be re-triggered until the longer duration has run out.