Is it possible to have a bowel movement and it cuts your anus and causes a pink color on the toilet paper after wiping, or should i be worried?

Yes: Hard stool can injure the lining of the rectum and cause bleeding, this is called a rectal fissure. Increase the amount of fiber in your diet (fruits, vegetables, whole wheat bread), can also use a fiber preparation like Metamucil, which any drug store can supply without a prescription. Rarely surgery is needed for long term fissures not responding to fiber.