The most common causes of dog muscle spasms are physical or neurological, but viruses, toxins and disease can cause similar symptoms. In the dog, tendon, bones and muscles form a complex and interconnected system designed to propel, support and protect the animal.he most common causes of dog muscle spasms are physical or neurological, but viruses, toxins and disease can cause similar symptoms. In the dog, tendon, bones and muscles form a complex and interconnected system designed to propel, support and protect the animal.