I get mild nosebleeds every time I remove a booger from the same spot in my nose. Why is this?

Irritation. Nose-picking is a top cause of nosebleeds. When you feel the booger there again, rather than picking it out, use saline spray to loosen it then blow your nose gently. Repeatedly inserting your finger into your nose is stopping the area from healing properly. Also, try some moisturizing agent like saline gel for that area inside the nose.