@AltarMantis You inspired me to make a whole separate post about this! I'm going to start a thread with this exact thing written except the parts about your individual mantis
I wouldn't suggest amputating it. The mantis can, once she regains her strength, hopefully chew off that part of the exoskeleton. If not, I would try using a moist q tip to wet it and gently peel it off, or just leaving her be for the moment. Additionally, I would NOT recommend amputating two legs in any scenario. I would say one leg missing is okay, but two legs missing can be dangerous, especially for bigger mantids. They need to hang upside down to molt, and having only two legs can result in falling during molting or just the inability to hang upside down. Many have tried taping or adhering their mantids to the roof of their cage just before they start molting to ensure that they carry through as a last ditch attempt to save them, but 99% of the time it ends in disaster as the mantis struggles and ends up harming itself and usually killing itself.
If you do decide to amputate, however, here's how. First, I would suggest some surgical scissors or very small, sharp scissors that can make small but precise cuts. I would suggest sterilizing them by either boiling water and letting them soak for at least five minutes, or filling a bowl with subbing alcohol and letting them soak for at least fifteen minutes. Either way, dry them off with a clean cotton cloth after you're finished and you'll have some clean sterile scissors. Then, find the nearest joint closest to where you want to amputate. If you amputate in the middle of the leg, it's harder to heal. In nature, the mantis would probably have that leg torn off at the softer and more easily healable joint. Make sure that the mantis can reach the place where the cut will be made with its mouth! Some suggest cooling the mantis in the fridge or freezer before the amputation to possibly reduce pain or make the mantis slower and calmer. If you decide to cool it, I would suggest the fridge for less likely event of accidental death. Then, take your scissors, make sure you're in the right place, and snip the joint as quickly as possible. You can use liquid bandage to seal the wound and prevent any bacteria from entering the wound. I've heard of wax (I've never tried it, so I have no idea how well it works, this is more of a consolidation) and superglue being used as well. For the wax, you melt it and wait until it's warm but soft and gently cover the wound with it. The superglue is pretty self explanatory. You can also let the wound heal on its own and scab over naturally.
Amputation is usually only necessary when an infection starts to form at the very tip of the limb. This looks fixable without such a drastic alteration as an amputation. Of course, you know your mantis and what will be the best for her health the best, so make your choice based on what you believe will help her survive. Best of luck!