Kevlar is not very good for cuts at all.
Let's ask Dr. Science. Remember, he's not a real doctor.
Kevlar fibers strongly resist stretching and breaking when stretched. A bullet is blunt and tries to force its way through a piece of cloth by stretching the fibers until they break. Kevlar is, thus, quite bullet resistant.
Kevlar is very, very common in fiber optic cables. The actual fiber itself is remarkably flexible. But, it is made of glass and if you pull on it, it will shatter and break. Even if it doesn't break, it can crack internally which is equally devestating to an optical cable. Fiber optic cables very often incorporate kevlar in their jackets. Kevlar strongly resists stretching. So, if you pull on the cable, the jacket will not stretch and you will not end up pulling on the glass fiber itself.
By the way, contrary to what you see in the movies, bullets do not bounce harmlessly off of kevlar garments. People shot while wearing kevlar garments just about about always suffer sever bruising from the impact. They often have soft-tissue damage. Cracked and even broken ribs sometimes result. Even internal injury can happen. Being shot while wearing a kevlar garment is not unlike being punched by a skilled boxer. There is a very strong impact.
What kevlar garments very often do is stop the bullet from penetrating and causing substantial internal dammage and substantial bleeding. A kevlar garment can often reduce a speeding bullet to a strong punch.
You see, when the bullet hits a fabric, it tries to stretch the fibers until they break and then the bullet continues through. But Kevlar fibers strongly resist stretching and breaking due to over-stretching. So, if the kevlar is unwilling to stretch and break, then the bullet is unable to penetrate.
Kevlar fibers are, however, not overly resistant to being cut by a blade attacking them perpendicularly. Kevlar fabric can be cut with a good pair of scissors. Technicians installing fiber optic cables routinely cut the Kevlar with scissors or a knife.
Kevlar fabric can be sewn conventionally. It seems remarkable that a fabric that can stop the proverbial speeding bullet will not stop a sewing needle. But a sewing needle does not really penetrate the fabric as much as it just slipps through the spaces between the threads. Kevlar fabric is a woven material woven from Kevlar fibers. Just like any fabric, there are spaces, albeit small spaces, between the fibers where a needle can slip through.
Many knives also have very fine, needle-like tips. They can stab right through kevlar fabric. Yes, the fabric that can stop a bullet can be defeated by a pocket knife.
So, there you go. Everything you ever wanted to know about Kevlar.