I just started dating this guy and found out that he is my grandmother's cousin's grandson... does this mean we are related by blood and that we can no longer date? Help!

You are cousins but at least 4 or 5 times removed, and if there is doubts, ask older family members since they are the ones who may freak out. They shouldn't but you never know.

Yes it is possible that you are slightly related. But no unless you are first cousins there are no laws that stop dating. ( some areas don't even regulate that)

But it is so far removed there is no issues at all