Is it correct to say
This way we can mutually practice together.
Since mutually has already been mentioned, is it correct if I use the word together at the end? It may be redundant, but is it wrong?
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Redundancy is not wrong. Redundancy is merely redundant.
That being said, the statement is not redundant, it is nonsensical. You cannot practice mutually in the first place. You can practice together, though.
Mutually is unnecessary here. Merriam-Webster has a definition of the base adjective mutual:
directed by each toward the other or the others
But one can't direct the action of practicing toward another, in the same way one can direct, for example, the action of giving a gift. Consider:
I gave a gift to her.
*I practiced a sonata to her.
It is generally only this sort of directed action that can be done mutually.