Alpha particles are helium ions. They are very damaging, but they are very easily stopped. A sheet of paper would protect you from alpha radiation.
Alpha radiation can damage DNA if it gets close to it. You‘d have to swallow or breath it in before coming to harm. Recently, the death of Russian Spy Alexander Litvinenko showed how devastating alpha radiation can be.
Alpha particles cause lots of damage to DNA. The damage is difficult to repair and some of our researchers are using this to study what happens when cells suffer multiple damage events close together. This site will also help you understand how cells try to repair damage.