You cannot inflict Persistent Damage just with Might by itself, at least according to the rules (you could try to convince your GM, as always in Open Legend).
However, a lot of forceful weapons can inflict the Bane with a Bane Attack or with extraordinary success (10 points over defense), which means you can use Might to cut someone’s arm off to inflict Persistent damage, you just need a fitting weapon to do it.
Btw, i asked a question about this previously and there you can see that the Bane Attack for Persistent Damage even gets advantage 1 and on both the Bane Attack and with extraordinary success you can inflict the Bane one Power Level higher than your attribute would normally allow for, if you use the correct weapon that is of course.
You can always make an axe that has Persistent Damage as a Bane, just make sure the GM has no reasonable objections.
By default, might can not, but Agility is by no means the power attribute compared to Might. There are a few feats that are along the might line as well.
If a weapon has “Persistent Damage” listed on it along with “Forceful”, this means might can be used to inflict. The banes you can inflict with exceptional success have to be ones you have access to in most cases. The GM could allow others that make sense with the narrative or thematically for combat/situation.
As far as the “cutting an arm off”, that isn’t something that should be happening too much except maybe by Lethal Damage. Most “hits” to HP are not really hits, but wearing your opponent down. Think of HP as stamina or grit. Lethal Damage is where your body is actually taking a blow. If you cut off a person arm they are probably going to be out of the fight and possibly die from shock.
For me, I allow Might to access persistent damage in my games and flavor it as internal bleeding (vs external for Agility). But that is a GM ruling, and not in default core rules.