Yes, dogs can eat beets. The previous answerer has got it all wrong. While it's true that dogs eat meat, dogs are not carnivores, they are omnivores just like us humans.
Being an omnivore means that you can eat both meat as well as vegetables.
Beets are actually one of the best vegetables to feed your dog. They have an impressive nutrient content.
The only problem with beets for dogs is that if they eat too much, then it can upset their stomachs and cause diarrhea, so don't let your dog eat a lot of beets at once.