It doesn't happen automatically. If you were served with a subpoena and you fail to appear, the state, if it chooses, can ask the court for a rule to show cause why you shouldn't be held in contempt. If that happens, the court would hold a hearing on the rule. You would have an opportunity to explain why you failed to appear, if you attend the hearing. If you fail to attend the hearing, then the court could issue a warrant
I don't know whether you have a subpoena for trial or for deposition, but either way, a subpoena is basically a court order that compels you to be at the place on the date and time listed in the subpoena. If you do not go to court, either the State, or defense attorney if it was a defense deposition subpoena, could ask for the Order to Show Cause and you could ultimately end up arrested for your failure to appear. It doesn't happen often, but it can happen.
A subpoena is a court order, not an invitation. As the other attorneys said, if you fail to appear, the judge can bring you before him on a "rule to show cause" hearing. This hearing is basically an opportunity for you to explain to the judge why you failed to appear. However, it's not often that the State pushes their witnesses in this way.