Oh wow, I had a slight feeling that that is what you meant but thought I was being silly. Um first of all, why would you want to give your heart to someone? When people say to each other that they have their heart, usually that mean's metaphorically not physically. But to answer your question, no that is not possible. The heart is a valuable organ to the body. It's function is essential to life so if someone were to cut your heart out I'm pretty sure you'd die almost instantly