I've never heard this expression. What is the source? It seems to mean that he stopped being friends with her but is sounds unusual. Knowing the source would better help one to answer your question.

Where did you hear this 'expression'? It doesn't sound like a real English expression to me. I'd understand what it means, but it is not something which any native speaker would say.

Yes, Brainer it does mean "not to talk to someone anymore". A better sentence would be; 'John's acquaintance with Jennifer ceased.'