Time Machine stores its backups as plain files and folders. All you need to do is go into
Backups.backupdb/yourComputerName/ and you'll be presented with a set of folders named in
yyyy-mm-dd-hhmmss format. Simply locate the most recent (or sort them - the most recent will be at the bottom, thanks to its name) and copy it elsewhere. You can then delete the Backups.backupdb folder or wipe the entire drive as you wish.
Alternatively, if you want to copy stuff from your old Mac to your new Mac, you should be given the option to restore from another Time Machine backup when Setup Assistant comes up on the first start up after a clean install (if you've already set up your new Mac, you can also do this after the fact with Migration Assistant in
/Application/Utilities/). After it's done that, it'll give you the option of re-using the Time Machine backup as the Time Machine location for your new Mac, so all the history will still be there, and will be gradually deleted once your external disk fills up.