There are two ways to kill a counselor as Jason. The first is to simply approach them and press RT to swing your weapon. It will take several swings to kill them, unless they have already been injured.
The second is to grab them (with LT) and wait a short moment for the execution kills to become available, then press one of the face buttons to perform the kill. Each face button corresponds to a different execution from among those you currently have equipped, or, if you are close enough to an environmental hazard, one of the buttons will allow you to perform an environmental execution. Note that some executions take longer to ready than others, and while you are holding a counselor you are open to being stunned by another or having them break free. Try to target counselors that have been running from you for longer, as they will have less stamina and be less likely to be able to break free before you can execute them.