I recall seeing this TV show when I was younger, probably a repeat (the sets and dress looked like a 1960s or perhaps even 1950s); I think it was an episode from a science fiction series, but can't be sure. It was in black and white.
The opening scene shows a group of people in white coats sitting at science stations (probably meant to be computers) in a white, ascetic-looking room. Suddenly -- as in, he's not there, then in the next frame he is -- a man appears and starts smashing the computers with an axe. He's subdued, but when the rest of the compound is searched several anomalies are found, including a motorised cart with the body of another scientist in it driving in small circles outside the research complex. The dead scientist was in the room with the rest of them the moment before the vandal appeared.
When the vandal is questioned the show jumps to tell his story: he was working merrily away when time stopped for everyone except him and the dead man, whose action was what stopped time. He did it deliberately, I think as part of an alien invasion. After trying to stop the traitor, he finished up outside armed with a machine gun, with the traitor in a cart. Because the traitor can manipulate time (a power granted by the invaders to help them) he's always somewhere other than he seems to be (where he was when he said whatever he's saying), so the vandal starts shooting in a circle, ultimately hitting the traitor, who's in the moving cart. He then goes back into the lab to destroy the equipment and start time again.