Generally you should always keep that very last couple seconds of the host saying your name and bringing you up so the reviewer can see how you really start your set.
(There are exceptions and I know some people very successfully start with a Bulletproof joke to get the crowd warm and then start the tape at the second bit)
In many cases, it's fine to cut off before the dismount. If you have a 15 minute spot and do your submission 5 up top and cut the tape there, that's often acceptable to a club Booker.
Just make sure it isn't abrupt. Sit in the laughter for a beat longer than usual before moving on.
For TV and many festivals, make it completely self contained. The tape and the spot should be exactly the same - from walking on to dismounting.