But I'm not sure what you mean by 'starting with a clause'--and both of your sentences have action at the beginning.
If you were talking about starting with -ing verbs, I'm totally on board with you there. It's not stricty ungrammatical (although it can lead to problems--see below), but it's often overused by beginning writers.
I agree with Jan for the reason and example she gave.
But, to reiterate, here is NOTHING WRONG with beginning with an adverbial phrase or gerund phrase or any of the clauses. It's even recommended for sentence variety and interest. BUT you do need to understand WHAT you are modifying by the clause or phrase or you'll run into a heap of trouble.
I will be covering this in the Grammar Forum in the future.
And I really want to encourage you all to read / participate in the Grammar Forum.
I've been able to read entries in the last few months, more than I've ever been able to in my history at FW, and dare I say I am appalled at the lack of mastery of "basics," even among the Masters.
There. I said it.