Can you cast a commander that was exiled by Darksteel Mutation from the command zone?

Darksteel Mutation is an Aura that, when the enchanted creature would be destroyed, causes it to be indestructible instead — it does not exile the commander. The commander stays on the battlefield as a 0/1 indestructible Insect artifact creature that loses all other abilities. So the premise of the question needs a small correction: Darksteel Mutation does not exile the commander; it traps it on the battlefield.

If somehow the commander enchanted by Darksteel Mutation does go to exile (e.g., via a different effect like Path to Exile), the commander replacement rule (CR 903.9a) gives the commander's owner the option to move it to the command zone instead of exile. If they choose to redirect it to the command zone, it is never actually in exile — it goes directly to the command zone.

From the command zone, the commander can be cast normally by paying its mana cost plus any commander tax (CR 903.8). So if the commander ends up in the command zone via that replacement effect, yes, you can cast it from there on your next available opportunity.

The real danger of Darksteel Mutation is precisely that it does not send the commander to exile or the graveyard — it leaves the commander stuck on the battlefield as a harmless Insect, and the opponent cannot easily use the command-zone replacement to escape it. Only effects that would move it off the battlefield (like sacrifice, bounce, or exile effects) let the owner invoke CR 903.9a.

Example: Your Atraxa is enchanted by Darksteel Mutation. She is now a 0/1 indestructible Insect with no abilities. Your opponent casts Path to Exile targeting Atraxa. Now CR 903.9a applies: you may choose to put Atraxa in the command zone instead of exile. If you do, you may later cast her from the command zone for her mana cost plus commander tax.