It kills or mutates cells wherever it is transported. While alpha particles do not penetrate much, they pack a lot of energy (~4.5 Million Electron Volts).
A classic case of alpha mortality happened during WWII. Young women who painted aircraft dial numbers with luminous paint that contained Radium 226 developed some serious symptoms, because at that time in their lives they were taking up a lot of calcium. Both calcium and radium are in Group IIA of the periodic table, and the body did not discriminate. Radium was transported to, and incorporated into growing bone. The bone marrow was irradiated. Upon autopsy, some many years later, micrographs revealed "Alpha Tracks" (Burns or trajectories of damage) left in the bone structure by the particles as Radium decayed.
Thorium 210 and 232 are suspected as being the primary cause of lung cancers in smokers, because thorium is a natural contaminant in Superphosphate fertilizers used in tobacco growing. A geiger counter stuck into a bag of 5-10-5 will show an above-background reading.
A huge "slug" of polonium 210 will cause a lot of trouble, and the timeline is about right, based on rat studies.
Thank-you!