1. To reduce slowly with time, work or effort, to diminish gradually. Literally it means to decrease through work. This phrasal verb is used for payment of a debt by installments. It is similar to pay off. If you are overweight you could work off the extra weight through diet and exercise. If someone was angry they might work off the anger by taking exercise.
For example: You can work off the debt in twelve installments.
I need to work off these extra pounds that I gained over Christmas.
After the argument he went for a walk to work off his anger.
2. To work one's tail (US), butt or arse off (UK) is an informal expression that means to work very hard. To put a lot of effort into something.
For example: He worked his arse off to get that promotion.
He worked his butt of doing that project.
I spend my life working my arse off and I never have anything to show for it.
Notice off work is a phrase we use when someone is ill and cannot work. John's off work with back problems.