How to tell my mentor to be careful when discussing my work in progress around people I do not trust? I had a very bad experience with a colleague and just do not like/trust him. (Eavesdropping, lying, ...) I am working on a project with my mentor, and know they shared information with the colleague I do not trust. How can I politely point that out to them?
If you can trust your mentor, just tell them. Say it as it is. But not in an email. This requires personal communication. 

But, if you cannot trust your mentor then you have a bigger problem than you state and need to find better guidance.