Premiere doesn't cut the media on disc, or copy the parts anywhere. It references the media on-disc and uses the bits that you include in a sequence. So to do that, you'd need to export the section that you want to a new file, then delete the original full file.
Normally you don't do this til you've at least finished your rough cut...
You can use project manager to consolidate your sequence (but not individual clips) and use handles to add any additional frames at the begining and end of the clip used. However, drives are so cheap now, do you really need to do this? Remember when the original clip is gone, it's gone and if you need to go back to it... you can't.
also, if you do a consolidate, make sure that it worked properly before you delete the original media. I've never done this in premiere, but did it a number of times in fcp7 (or earlier versions of fcp) and occasionally there might be an issue with the integrity of the consolidate.