Sometimes cymbals can be damaged in transit, that's why I always recommend that they be carried and stored in a well designed bag or case. If cymbals are dropped onto a hard surface it could also cause them to crack. It is, however, unusual to crack a ride cymbal under normal playing conditions if the ride cymbal being played within the volume thresehold of it's diameter and thickness (weight).

Some cracks can be
"stop drilled". That means drilling a small hole at each end of the crack to "STOP" it from spreading. Small cracks like that may not cause a big difference in the overall sound
OR the edges of the crack could rattle against one another producing a buzzing sound. Who knows until you try to fix it. Sometimes the cymbal can be usable......sometimes not.

If you have basically knocked a hole in the edge .....or otherwise knocked several cracks and splints into the surface....then YES it can be cut out as an attempt to stop future damage. It will most likely not sound good to you anymore.......unless you're wanting a weird and probably ugly sound.
I believe the most urgent matter is to determine EXACTLY WHY IT CRACKED. That's important if you don't contine to shatter good cymbals. If it's not important, then you can skip the rest of this reply.

Other than an accident from dropping it or some transport mishap, I hope the damage wasn't a result of bacically beating the hell out of it.
let me use a real example in venue size/volume requirements. I played six shows shows with an 18 piece big band before 10,000 people at each performance last week. I used right and left overhead mics to make sure my cymbals were clearly in the mix. I did not play them any harder than I would typically play on a big band gig. I'll perform a small venue jazz performance tomorrow, and will select volume appropriate cymbals for that situation. I won't need to mic them in the jazz venue. My point is that if you must carry a large room with volume you need sound reinforcement not sledge hammer sized sticks.
As I have discussed before, cymbals
do have a volume threshold. That is the point where hitting them harder doesn't produce any additional useable tone or volume. Beyond that point you will most likely crack or bend the cymbal.
So if you have cracked a cymbal as a result of trying to extract more volume than the cymbal was capable of producing, then you need to select cymbals designed for very hard playing and extreme volume. For those cymbals I also seriously recommend on stage ear protection.
Here is a blog I wrote that you also might find helpful.
http://www.drumsoloartist.com/live/blog/view/id_121/title_taking-care-of-your-cymbals/