I just tried this in Live 8.2.2. I started in session view with a MIDI clip containing notes, as well as modwheel (CC 1) and stuenuto (CC 66) data in it as envelopes. These are envelopes in the clip itself, not on the timeline - because we're in session view.
I couldn't find any way in the clip editor to select both note and envelope data simultaneously. However, splitting/consolidating in arrangement view worked for me - I produced a clip with the envelope and note data moved around together. Here are the steps in detail:
Drag the clip to an empty area of the arrange view (click and drag the clip, then press tab to switch to arrangement and drop). I put it on the same track, but I suppose any other MIDI track would do.
On the arrangement editor use the split command (cmd/ctrl+e) at the location where you want to cut the clip. The clip will split in two.
Drag the clips so that you have them arranged how you want.
Consolidate the clips (cmd/ctrl+j)
You'll now have one clip, with all the note data and controller data moved over. It's still a MIDI clip that you can edit - it's not bounced to audio. Click and drag that clip back to the session view and you should be set.
The method is, of course, not perfect - if you wanted to have a note sustain past the split point, you'll of course not be able to do that because the split cuts everything off at that point.
Conceptually, I suppose you could split your clip into two clips on separate tracks, edit to taste, and then route their MIDI outputs to another track and record - effectively resampling the MIDI data - although I've never tried it and I suspect it's a bit more elaborate than what you're looking to do.