Is it common for dentist to put a child completely sleep to do work on her?

Sometimes. Depending on the age of the child and the amount of work to be done they might. However if you feel uncomfortable with this you may want to get a second opinion.
No. If the child is unable to be cooperative for needed treatment, some form of sedation / relaxation is often used. Total general anesthesia is not common nor recommended unless absolutely necessary.
Somewhat. This is a common practice for a child who needs a lot of dental work such as pulpotomies and crowns on almost every tooth. It's so sad to see a child with rampant decay on almost every tooth, but I have seen it. A pediatric dentist will often opt to do all this work at once under general anesthesia. This is also done for unruly children who have dental work and there is no other alternative.