There were many perpetrators of the various mass killings that happened during World War II. The most famous mass killings were what we now call the Holocaust, but there were others. Some of the perpetrators were military, some were paramilitary, and others were simply civilians.
Some of the mass killings were carried out by paramilitary units. For example, one non-Holocaust mass killing was the killing of Polish officers and others by the Soviet Union at Katyn Forest. This killing of over 20,000 military officers, police officers, and intelligentsia was carried out by members of the Soviet secret police, which could be seen as a paramilitary group.
Other mass killings were carried out by more formally military units. When the Germans occupied various areas of Europe, they tended to carry out mass killings in reprisal for any actions taken by partisans against German soldiers. These mass killings were often carried out by German soldiers. Many more mass killings were carried out by the SS, which was essentially a military organization, but which was formally separate from the German Army.
Finally, even civilians were part of some mass killings. These include civilian doctors and scientists who participated in devising the means of killing. They also include civilians in captured areas like Lithuania. Some civilians participated in mass murder of Jews in riots or pogroms against them.
Thus, we can see that the mass killings in WWII were carried out by a variety of actors.