Can you cast your commander from the command zone if it was exiled by your opponent's spell?

When your commander would be put into a graveyard or exile from anywhere, you may choose to move it to the command zone instead — this is a replacement effect defined by the Commander format rules (CR 903.9). The key word is may: it is your choice, not automatic.

If your opponent casts a spell that exiles your commander (such as Swords to Plowshares), you are given the opportunity to apply the replacement effect and redirect it to the command zone instead of exile. If you choose to do so, it goes to the command zone and you can later cast it from there, paying its commander tax (CR 903.8).

However, if you do not make that choice — or if you miss the opportunity — your commander actually ends up in the exile zone. Once it is in exile, it is treated as a normal exiled card. It is not castable from exile unless some other card effect specifically allows casting from exile (CR 400.1, 903.9).

Concrete example: Your opponent casts Swords to Plowshares targeting your commander Atraxa. As the exile effect resolves, you must choose: let Atraxa go to exile, or redirect her to the command zone. If you say nothing and let her go to exile, she is stuck there — you cannot cast her from the command zone because she is not in the command zone.

So the answer depends on your choice at the time the effect resolves. If you redirect to the command zone via CR 903.9, you can cast it later. If you let it go to exile, you cannot cast it from the command zone.