Is It Harmful to Pull a Dog Across the Floor by Its Legs?

Your instinct is right. Pulling a dog by the legs puts strain on the joints and ligaments of the shoulders, elbows, hips and knees, and it can cause or worsen a sprain or other joint injury, especially in heavier dogs or dogs with joint problems. It can also make a dog fearful of being handled.

Gentler ways to move a dog include calling her over, using a treat, or lifting her properly with one arm under the chest and one under the hindquarters; for a 60 lb dog, it's safer to have two people lift together. For a heavy dog, a towel or sling under the belly works well.

See dog sprains and strains.

This is general information, not a diagnosis. Please follow your own vet's advice.