Could a muscle spasm cause pain in the mid back when you take a deep breath?

Yes: Muscle spasm is common. You could also have inflammation in the chest cavity. If you have cough or fever see a doctor for evaluation.

Yes: Yes, it can. But, there are also other potential causes. If you've done recent heavy lifting/strenuous exercise, etc, then this is very much possible. If you are having any chest pain, shortness of breath, or fever, however, you should see a doctor ASAP. Best wishes.