Danger is a relative term. In general for beta-emitters it's not dangerous to be in the same room. Even a relatively hard beta, like P32 (around 1.7 million electron volts) will not penetrate its container. If ingested and absorbed into the body, however, the beta-emitter will be in close proximity to the other molecules of the body. So its energy can cause disruption of those molecules. Even a relatively soft beta, like tritium's (around 15 thousand electron volts) can cause problems if enough is ingested. One damage mechanism is mutations. Another is formation of poisonous compounds such as free radicals.
Nucleic acids (RNA and especially DNA) carry information regulating the functioning of the cell. Radiation-incduced mutation of the DNA could cause the cell to behave badly, such as multiplying without control, forming a cancer.