'Doing' something with something means sich mit etwas beschäftigen, etwas machen. In the context of TV shows, 'tape' is the celluloid medium on which you record a show.
Possible meanings in this context are that the speaker is working with the tape that day:e.g.
as a video tape operator: http://www.media-match.com/usa/jobtypes/video...Or
(as this is the director) telling the video tape operator when to stop and start: http://en.wikipedia.org/wiki/Television_directorOr
my first suggestion, which I think you didn't understand. No, I did not say it means 'archivieren'. I said that perhaps the director is saying 'Today I am not broadcasting a live show. I am playing a taped show.'
I don't know what you found on Google but I don't see anyone offering to 'do tape'. I see the Can-Do National Tape Company, selling adhesive tape.