You are referring to Verizon Cloud, correct?
If you sign into My Verizon there is a Manage Products & Apps page. Go to the tab that says "Manage Your Products" and select the line you would like to remove cloud from. Listed under Verizon Cloud, in the upper right hand corner, there is a link to "Remove from Account."
Do you subscribe to the cloud separately or are you on a More Everything plan? If on the first, the instructions above are correct, if on the latter, you just disable the Sync and Cloud apps on the phone, and remove the Verizon account from the phone under Settings-Accounts.