So I did some digging through canon for plasma projectors and the only thing I could come up with was
this. Since you're definitely not getting the desired effect out of
that, I'm going to assume you're utilizing the next best thing, which would be a plasma monofilament that would give it a cutting edge akin to a lightsaber.
That still doesn't give it the ability to cut through Beskar
easily, though it may give it the ability to do so over time. The problem with that is that Cortosis in its unrefined form is extremely brittle, and would be compromised very quickly when striking Beskar. Refined, it would wear down much more slowly, but it's not going to speed up the process by any great amount.
I'm going to assume that you're utilizing refined cortosis, because in its raw form it would be impossible to slap a plasma filament on it due to the way the ore sabotages energy fields.
So, the surface of the axe overall wouldn't necessarily be hot, but the edge would be at lightsaber heat. You can revise accordingly, if you'd like.
"Can cut in the same way as a Lightsaber" would be a sufficient change. I'd remove the bit about Beskar, though; as a Lightsaber can cut through the metal over time, you still get what you want out of the deal but it's not happening at any extreme rate.
To be even more blunt, you're hitting with a plasma filament almost 100 percent of the time. Using cortosis actually weakens the overall potential of this weapon. The heavier the axe is, the more potential damage you get. You'd be best served by durasteel, duranium, impervium, beskar, neuranium- any number of heavier metals that would afford it that extra oomph.
Against a weapon that's heavier and resistant to plasma, this would realistically start to deform after several strikes. Coupled with that and the fact that you'd only benefit from the cortosis while blocking with the flat of the axe, you're much better off opting for a gauntlet or some armor that has the ability to short out lightsabers, separate from your weapon.
Also, with a plasma filament, the entire weapon wouldn't be covered in plasma, so you can remove that strength. The overall heat of the weapon with a filament wouldn't be unmanageable enough to make it a weakness either, so that could also be removed.
Let me know what you think.
Be'iqaronn