2.) so does the mind.
It's a correlative conjunction. In other words, think of it like a "conjunction phrase". "Not only...but also", "just as...so", "whether...or".
"the mind does too" isn't part of the collection of phrases and would be better suited for something like, "A person's body ages at different rates. The mind does too." or "A person's body ages at different rates and the mind does too." for a bit of emphasis.
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