There is a 'hand' tool called a Grout Tool that you can buy at any plumbing store, tile store, or Home Center for a few $$$. Besides, you DON'T have to go all the way down to the base to clean out the old grout. Go 2x's as deep as it is wide.
THere is a mechanical tool but you run the risk of damaging your tiles if you're not good at it. Try the hand tool first.
And next time, before you use a hammer and chisel on ANYTHING, ask because you could do more damage than you'd like. My best to ya and hope this helps.