How would having their arms cut off affect their ability to fight? Yeah, you kind of need those. Without them, you really can’t. I’m sure there’s a few exceptions out there, like the one armed MMA fighter, who’s name is escaping me at the moment. But, cutting off her arms is going to be the end of her military career. She’ll be packed up and shipped home to a hospital, and her combat days will be over.
Obviously, if this is a science fiction setting, and we’re talking about cybernetic augmentation to replace the lost limbs, that’s not going to apply. The same is true if it’s a high magic fantasy setting where she can have living arms of wood grafted onto her, or whatever. But, any historical setting, and even modern day, that’s not an option.
In daily life? You can look at actual amputees, and see how they function. I know I’ve seen a couple pretty good documentaries on the subject over the years, but I can’t identify any off hand. If that’s not an option, just take a day and be very conscious of everything you do with your arms and hands. Then realize your character probably can’t do any of them without prosthetics. That means no opening doors, no feeding themselves, nothing.
Prosthetics make that a little easier, and there are some people out there who can do fantastic things with theirs. Which could, with time and practice, allow her to feed herself, open doors, and operate in civilian life to some extent. But, how does this affect her ability to fight? She can’t.
Also, you’re not going to have a military officer that uses melee weapons. That just doesn’t happen, for basically the same reason you won’t find a bayonet charge on a modern battlefield. People have guns, and it turns out, you can use guns to kill people at slightly longer than arm’s reach. Meaning your “high ranking” whatever won’t be wading into battle and belting out, “drive me closer, I want to hit them with my sword!”
Also, high ranking personnel don’t actually see combat, if they can help it. If you’ve proved yourself valuable enough to be promoted, there are far more expendable soldiers available to take your place in the fray.
Someone in a command position may be technically replaceable, but, their loss would be disproportionally disruptive to any ongoing conflict. There’s a lot of truth to the whole “cut off the head and the snake dies” cliche when it comes to crippling a large military force. Without someone to tell the grunts where to go or what to do, they’re just so many tons of meat. And, that’s what rank ultimately means. It’s an indication of how far up the chain of command your character is.
Unless they’re in something like the Imperium of Man’s Astra Militarum, you’re not going to see someone waving swords around on the battlefield, and you’re not going to see high ranking officers wading into combat. They have a job to do, and it doesn’t involve getting waxed by the first enemy sniper they can find.
@kalany, So, turns out, I did misread the question. Mea culpa, for what little that’s worth. Unfortunately, it doesn’t really change much about the answer. If their character is still engaged in front line combat, they’re going to need both arms to function. You can’t just lop one off and call it cool.
You need two functioning limbs (not counting legs) to fight something with two functioning limbs (again, not counting legs). You need two functioning limbs to operate a rifle. You can’t one hand them. You need two functioning limbs to reload any firearm. And, of course, saying, “but I wanted to hit them with a sword,” just isn’t a valid tactic in the 21st century.
Now, if their character was already a flag officer (an Admiral or General), who wasn’t involved in combat… just forget that whole melee thing, then wandering around with one arm isn’t unprecedented. There are examples like Lord Nelson, who continued belting out orders after he’d lost his arm, and I think his eye. But, as I said above, these are people telling others where to fight, not doing it personally. After all, the art of command is delegation, not demonstration.