ionising atom(s) with gamma rays
Various mechanisms for interaction of gamma radiation with matter are possible. Depending on the energy and the composition of the absorbing material, the most important types for gamma radiation are photoelectric effect, Compton scattering, and pair production.

In absorption of gamma radiation of lower energy by the photoelectric effect, the photon is absorbed completely by the atom and an energetic electron is ejected. The energy of the emitted electron is the difference between the energy of the gamma-ray and the binding energy for that electron in the atom.

Gamma radiation of higher energy directly interacts with one electron by the Compton effect. Usually, this is the most probable interaction of gamma radiation. The incoming photon transfers a portion of its energy to the electron and is deflected through an angle with respects to its original direction. Since all angles of scattering are possible, the transferred energy varies from zero to a large fraction of the energy of the photon. The scattered photon may have sufficient energy to interact further by Compton effect or photoelectric effect.

If the energy of the gamma radiation is very large (i.e. it exceeds $1.02\ \mathrm{MeV}$, which is twice the rest-mass energy of an electron), the process of pair production is energetically possible. In the interaction, the photon disappears and is replaced by an electron and a positron. The process may be considered as the inverse of positron annihilation.

Your additional question about the equivalent dose is slightly misleading. The resulting equivalent dose from gamma radiation is not particularly low. By definition, the radiation weighting factor of gamma radiation is $w_\text{R}=1$. Thus, an absorbed dose of $D=1\ \mathrm{Gy}$ leads to an equivalent dose of $H=1\ \mathrm{Sv}$. However, you may ask why some other radiation types have a higher relative biological effectiveness.