How to stop android phone from vibrate during the start up and the shut down?
Unfortunately this isn't something that can't be turned on or off.  It's possible that it's a vendor specific thing, you don't say what device you have or if you are rooted or not, so I assume this is the case.

I'm running a SGS3 with a custom ROM on it (AOKP) and I've just restarted the device and can confirm there was no vibration during the start or stop procedure.  However my Nexus One with a stock ROM did vibrate.

A possible fix is to root the device and stick a custom ROM on there, but that's quite an extreme fix for the issue.