The first sentence is grammatically correct. It is the simple present tense. However, we usually use the simple present tense to state a general truth. This particular action is more likely to be something that is in progress or continuous. [The dog is biting the man.]Originally Posted by Anonymous
The second sentence is grammatically correct, but I'd say using the passive voice in that particular context doesn't work very well. To me, it's rather awkward sounding.
I would rewrite it as follows: The dog is biting the man.
I hope that helps. :)