When something is " cut short " it is terminated before it is intended or before its full extent. Here cutting someone short is interrupting their speech before its proper end. Someone is talking and the other suddenly interrupts his/her speech. So the person is apologizing for having done so.
In this sentence it is an instant remark probably referring to cutting a speech short.
In general 'cutting someone short' could refer to the disruption of someone's activity whatever it is ( it could be speech or while doing any other activity ).