Your proverbial heart? Or, your physical heart?
The answer, of course depends not on which heart you mean, but which mind you mean?
Referring to the phrase, "he's lost his mind" we can gather that if you did lose your proverbial heart, you could only lose your 'mind' as in, your sanity, depending on what choices you chose thereafter.
With the mind as in the 'ego' the thought processes that sometimes control us, if you lost your proverbial heart , you would more than likely lose your mind as it was because then you wouldn't function as a typical human anymore. You'd become robotic, lacking empathy, compassion and other human traits that influence the mind and make you human. You would become a machine, and their minds are something completely different. The question would become, what would be the driving force of your new state of mind? What would influence your decisions?
If you meant losing your actual, physical heart... well, then I would say yes and no to losing your mind, any mind.
Yes, because you would be dead. Your body as you knew it would no longer be functioning on any level, and therefore be without mind.
No, because it is said the 'mind' never dies, but overlaps from reincarnation to reincarnation, which explains why we carry some habits and memories through, often being perceived as genetics, dream states or deja vu. Although it is actually your spirit or soul that is doing the reincarnating, the soul comes from the one soul that inhabits everything, and so your 'mind' that learns more with every reincarnation is actually your very individualism. Without it, you are not you.