Mind is a function of the brain.
In fact, the mind is only
ONE function of the brain. The conscious mind is more-or-less resident in the forebrain, the large mass of brain tissue that is several times larger than the corresponding region in the brains of the other species of apes.
But many of our memories are stored in the midbrain, which is below the forebrain but above the hindbrain. The forebrain and the midbrain can communicate, after a fashion, and this is how we are able to access old memories. It's also how the new thoughts and experiences we have during the day are organized and stored in the midbrain. This takes place during R.E.M. sleep.
The discovery of the technology of controlled fire a couple of million years ago by one of our ancestral species caused a quantum improvement in our brainpower, because campfires kept the predators at bay, allowing us to sleep longer and more restfully--allowing us to organize our memories much more effectively. The domestication of dogs made us even safer at night. We now have two periods of R.E.M. every night, with a total duration of 3-4 hours, and this is what allowed us to develop art, sophisticated stone tools and, ultimately, agriculture, which ushered in the Neolithic Era.
The rather small hindbrain, at the base of the head, is the much more primitive mammalian brain that keeps our heart beating at the right speed, regulates body temperature, keeps our breathing steady, has some control over our endocrine system (hormones, etc.), and generally takes care of the part of the brain we share with the most primitive vertebrates: the cartilaginous fishes, which include sharks, rays, eels, etc., animals that have skeletons but they're made of cartilage instead of bone. The brains in the modern vertebrates were actually outgrowths of the olfactory lobe. The cartilaginous fished succeeded because of their sense of smell, which told them where food was, and where larger predatory creatures were. This can be thought of as the first glimmer of intelligence in the first animals with skeletons--our distant ancestors.
As you see, the brain has a lot of responsibilities. The mind is only one part of it. In humans, it is a very large part, but in other vertebrates the more instinctive functions in the lower part of the brain play a larger role in their behavior. But even for humans, the brain has a lot of other things to do besides the "thinking" that takes place in the mind.
In any case, it is absolutely wrong to say that the mind = the brain. The correct statement is that the mind
resides in one part of the brain.