To 'save your skin' means to prevent yourself from enduring harm or difficulty. To 'save your skin' is to save yourself. If someone protected you or prevented you from harm in some way you could say 'thank you for saving my skin'. 

1. Thanks for saving my skin back there. I would have walked into the road without looking if you hadn't pulled me back in time.
2. I was lucky in the bike accident because my helmet and leathers saved my skin when I crashed.

1. I owe you one for helping me complete the order before the deadline. You really saved my skin!
2. Instead of taking the blame for her mistake, Jenny threw me under the bus to save her own skin.