"The Mechanical Mice" by Maurice G. Hugi and Eric Frank Russell
According to one review, here's the gist of it:
Dan Burman is a very rich inventor. 12 years ago, he had invented the
"Burman Bullfrog Battery" – the greatest known power source for small
portable devices. Now he has invented something new. Only he doesn't
know what it's supposed to do!
He seeks help from a friend, Bill, and during this discussion, Dan
reveals that he's not the real inventor of his famous battery or the
new device. He stole their designs from the future!
His only genuine invention is a kind of crystal ball he calls
"psychophone" – a virtual-reality time-travel machine that can take
you to the future. And since it is impossible to go back to same time
and place (again), a single session is all you have to learn what you
can about anything.
This is how the new machine came into existence.
That is when the device – sitting in the same room – automatically
springs into action. Arms stretch out to pick Dan's wristwatch...
It's a night of sheer terror. A jeweler is robbed. There's a
burglary at the precision instruments shop. Several cats are also
found dead on the streets...
Dan soon discovers what he has created: a robot programmed to survive
above all else, even capable of giving birth! The brood has been
snatching food and killing whatever comes in their way.
~ Edited from Variety SF
A short excerpt from the book. How Bill reacts when he first lays eyes on the machine:
It was a stunner. The thing was a metal box with a glossy,
rhodium-plated surface. In general size and shape it bore a faint
resemblance to an upended coffin, and had the same brooding, ominous
air of a casket waiting for its owner to give up the ghost.
Another passage, this time describing the tiny thieves...
A score of houses had been entered and four shops robbed by things
that had the agility and furtiveness of rats — except that they
emitted tiny ticks and buzzing noises.
One was seen racing along the road by a homing railway worker. He
tried to pick it up, lost his forefinger and thumb, stood nursing the
stumps until an ambulance rushed him away.
Rare metals and fine parts were the prey of these ticking marauders.
The story has appeared in a number of publications, including the three featured on top. Read more about it here and download a .txt file of the full story.