Speak sternly to the cat!

Find the mice tunnels. They are often 1-2 inches below, if you have beds, they will be running parallel to the bed side. Punch a hole with your finger from above, pour rat poison, then close. This will not prevent some poisoning of the soil, but it will prevent poisoning of the birds and other above ground critters. Rat poison should be biodegradable anyway.

Voles are as likely as mice, and they are more likely to eat veggies. You can catch them with little mouse-size snap traps, or get the cat on task. I do speak sternly to my mouser cat if he has work to do!

I'd never poison rodents where a cat or other carnivore might catch and eat them, ingesting the poison.

Cat is old I'm afraid, and won't accept another...

Yeah it's eating ALL of my tomatoes as soon as they even hint red, and all of the beets literally have tops but no beets like in the cartoons.

Looks like I'm off to buy mousetraps. And cover with boxes of some sort to keep out the songbirds.
Thanks for the help.

I have chipmunks who eat everything I have resorted to picking the tomatoes as soon as they start to turn color

Disappearing beets sure sounds like voles to me. Sometimes they will leave roots partially eaten with tooth marks. Don't want to gross anybody out, but if the narrow, squared-off toothprints fit, you will know your enemy.

I would go ahead and try using ground black pepper around all of your beds. This should help deter all rodents. Also planting herds such as oregano, sage, cayenne, and peppermint will help deter rodents. I would sprinkle black pepper and spray mint oil on the mulch and around rodent holes. Also catnip helps attract cats to your garden, they love the stuff. Just be careful because cats can tare apart a bed of catnip. Marigolds also deter a wide variety of pests, including but not limited to rodents. I line the edges of my beds with marigolds.