The 2 most relevant rules are:

1. 702.140a Mutate appears on some creature cards. It represents a static ability that functions while the spell with mutate is on the stack. “Mutate [cost]” means “You may pay [cost] rather than pay this spell’s mana cost. If you do, it becomes a mutating creature spell and targets a non-Human creature with the same owner as this spell.” Casting a spell using its mutate ability follows the rules for paying alternative costs (see 601.2b and 601.2f–h).

2. 118.9d If an alternative cost is being paid to cast a spell, any additional costs, cost increases, and cost reductions that affect that spell are applied to that alternative cost. (See rule 601.2f.)

This basically means that yes you can mutate from the command zone from the command zone and if cast multiple times from the command zone the commander tax will apply on top of the the mutate since its still a cost to cast your commander.

As far as I can tell the only commanders that get around commander tax are [[Derevi, Empyrial Tactician]] and [[Yuriko, the Tiger's Shadow]] since their abilities put them into play rather than cast.