You can reuse the old yeast, however, since meads are generally made with higher levels of alcohol than beers, there tends to be more selection/mutation pressure on the yeast and you may get drift that creates some difference in flavors if you reuse the same yeast multiple times. That could be good... or not. Reusing them once should not be a problem at all. If you do reuse the yeast, be sure to aerate them well as they will need to rebuild the sterols to allow more division.
Since I mostly use dry yeast, which are as cheap as dirt, I generally just pitch fresh yeast for the sake of consistent results.
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