Display only 1 cart in View Carts in Accounts

Is there any way to turn off the ability to save more than one cart to a users account? We only want the customers last cart to be saved or able to be added to in the Accounts->View Carts which would now just be View Cart. Thanks.

You have "multi carts" enabled, I guess?
The simplest way will be to disable it in the backend under -> System -> Configuration -> Features tab -> Main. Then each customer will have only one single cart.

Hope this helps.