Yeah, the same way the Gestapo dealt with law enforcement!
NKVD were the murderous thugs that did the political executions, oversaw the deportations of Cossacks and other nationalities that Stalin obliterated, shot deserters under Order No. 227, shot those who stopped charging ahead during the human wave assaults, etc.
They also ran the slave labor camps in the arctic and Siberia and executed all political and common criminals in Kiev, Brest, Lvov, Sebastopol, etc. in the face of the Nazi juggernaut before each of these cities was captured by the Germans.
The only legitimate part of the NKVD, IMO, were the OSMBON which were Motorized Infantry Brigades and were precursors to the Spetznatz.
For a good discussion about life under Stalin during WW2, read "Ivans War - Life and Death in the Red Army, 1939-1945 by Catherine Merridale.