No Ethel he C: drive is the drive that Windows is defaulted to run on so you cannot clean it whiel running Windows from it.
If you connect the drive you want clean to the machine thta is already running Windows it will be given a digffrent letter it will cease to be the C: drive it used to be if it had/has Windows installed on it. So it might be called D: or F: or whatever port it is connected to.
To make sure in DISKPART you have the right drive run DISKPART without the drive hooked up and see what disks are listed and then connect the old drive and then run list disk again and it will appear as a numbered disk. Disk is just the old term for drive. You then select that disk and use clean or clean all whichever you prefer the clean all does take considerably longer to do depending on the size of the drive.