You can certainly trim off all the dying or badly damaged leaves. If a leaf still has a good portion of healthy green on it, just cut off the damaged part, as any intact green leaf tissue will continue to photosynthesize and make food to support the plant's recovery. You can remove those leaves later when new growth has come along.
Cut as closely as possible to the crown, because leaf tissue left behind will rot, though usually small left behind bits won't cause any problems. When the plant has recovered and grown some good strong leaves, instead of cutting, you can gently peel damaged or old leaves away. This usually leaves no tissue behind. Think of how a head of celery or lettuce grows. If you pull a leaf or stalk off from the base of celery or lettuce, it will usually come off clean, leaving little or no part of itself behind. Same idea with the sword leaves. You can hold the crown down with one hand, peel off a dead leaf with the other. Best done on plants that are well established, so you don't accidentally tear the crown.
Generally there are just 3 types of plants in terms of how they grow. Crown growing, stem growing and bulbs. Not many water plants have bulbs, but Lilies, Aponogeton & Crinums do. The rest are crown or stem growers. Some have rhizomes, either above or below substrate, but rhizomes are simply a modified stem. Stem growers can be usually be propagated from cuttings easily. Some plants can even be propagated from simple leaf cuttings. Crown growers frequently produce runners with little plantlets. These you can grow on separately once they have some leaves and roots of their own, or leave them to spread as they please.
Swords all have crowns; all the growth comes from a central point. Most crown growers will rot if the crown is buried, so always leave the crown exposed above the substrate. Bury only the roots. Aside from the red coloured ones that need more light to keep their colour, swords are not demanding of a lot of light. Most of them will recover, even from pretty severe damage, so long as the crown itself is healthy and intact.
