Xavier could find her anywhere with cerebro, infact he could sit at the mansion and just chill out while he stops her, it's not that crazy
It took nearly all of Charles to use Cerebro (blows up) and even after that he had to look into Logan's mind, see his horrible future and then had to communicate with his future-self. It wasn't as simple as how you portrayed it. What he did was the exact opposite of just "chill"ing there...
Also he says in the movie why he couldn't control Mystique. He was powerless just a few hours (?) ago from Hank's serum: "she's not letting me. I'm barely holding on. I'm not strong enough yet."
But again back on topic, it was pointless for Mystique to destroy Cerebro as in:
the theatrical cut, they knew where she was going from that woman seeing her plane ticket;
from the Rogue Cut, although Mystique destroyed Cerebro, Xavier just decided for the trio (X, Logan, Hank) to go to Washington, where lo and behold, Mystique was gonna be, probably unbeknownst to Charles at the time of his decision.
So Mystique's infiltration scene showed that:
1) Beast as an idiot;
2) Mystique as unsympathetic and ungrateful. Probably also an idiot for going back to the mansion when she didn't want to be found;
3) Only point was to feature a showmance between Beast and Mystique which is only rewarded in the movie when the two wryly smile before Mystique leaves at the end of the movie.