depending on the context. "I will accept your heart only" can mean "마음만 받을게" which means 'no thanks' or 'I appreciate your effort but I am good'

Are you talking about the expression, "마음을 받아주다" :)? Yeah, we would usually hear this in romantic situations where one of a couple "finally accepts the other's proposal for marriage or dating," but we could hear it in many other different situations (business offers, recruitment offers, etc.) as well. Lastly, I think it sounds more serious & meaningful than just "Thanks, I'll accept it." (That being said, I don't know exactly what phrase you are talking about :).) Hope that helps!