Time Machine reset

I have been using time machine for more than a year and I would like to know how to cleanout the old backups and start anew. 

If you are absolutely certain that you do not need these backups, you can remove them by simply deleting the appropriate folders on the TimeMachine share on your My Cloud. There will be one folder per each Mac that is backed up so simply delete those whose backups you want to erase. TimeMachine will then create a new backup for that Mac when it is run the next time.