And before anyone tries to grab my goat about this...
This is one of those times when I see a saying and I am left wondering what type of situation led to this becoming an actual part of the English dialect. I rated you up just for the entertainment value possibilities of "grab my goat".
I have never heard of "grab my goat" as far as a phrase goes. I have heard of "gets my goat", which basically means something makes you angry. Getting someone's goat originated from the racetrack, where goats where kept with horses to keep them calm. So taking someone's goat would cause the horse to become agitated and run poorly. So, either due to it upsetting the horse or the owner, that's why getting someone's goat is bad thing.
Now, as for grabbing a goat, unless that is a euphemism for something else, I'm afraid I am at a loss.