If the court determines that you violated the supervision by virtue of the second incident, it can sentence you on the first case as though the supervision never occurred.
If you are arrested for a new offense during the period that you have been placed on Court Supervision, you risk having a violation (or Petition to revoke sentence) filed against you by the State. If this allegation is proven, you can be re-sentenced to either Conditional Discharge, Probation, or county jail time. Normally, once a violation/petition is filed, the Judge will continue the proceeding to see what happens on the new arrest - meaning, whether you are found guilty (by either plea or trial) or if the case is either dismissed or you are found Not Guilty. Obviously, if you either plea or are found guilty of the new offense, the State will have a much easier time proving the violation. If the new charge is dismissed (or you are found Not Guilty after trial) you have a chance that the Violation action will not be proven & you may remain of Court Supervision for the balance of the original sentence.