Does capsaicin from peppers actually cause tissue damage? If so how?

The heat is a "trick"
...the feelings we get are simply from our body's response, not anything the chilli is doing to actually burn us.

Possible side effects of capsaicin include:

Nausea and Vomiting

Capsaicin patches may help with pain relief, but their higher concentrations of capsaicin could cause problems for some. Nausea and vomiting are commonly reported side effects of these patches.

Diarrhea

Capsaicin is known to irritate the lining of the digestive tract, which could cause an upset stomach and diarrhea. It may also cause food to be digested too quickly, which can make your stool burn as it passes through your body.

Acid Reflux

Capsaicin could worsen symptoms of acid reflux. The sensation of heat it creates can irritate your stomach lining, possibly causing reflux, heartburn, and other issues.

Pepper spray, also known as capsicum spray, is a lachrymatory agent (a chemical compound that irritates the eyes to cause tears, pain, and even temporary blindness) used in crowd control and personal self-defense, including defense against dogs and bears. The active ingredient in pepper spray is oleoresin capsicum (OC) from chili peppers that is extracted in an organic solvent such as ethanol. The solvent is then evaporated, and the waxlike resin is emulsified with propylene glycol to suspend the OC in water. The OC is then pressurized for use in pepper spray.