No, you should never do that. It's extremely dangerous.
Your mower's exhaust contains poisonous carbon monoxide gas, which you cannot see or smell. In an enclosed space like a garage, it can build up to dangerous levels very quickly, causing unconsciousness or death.
Always start and operate the engine outdoors in a well-ventilated area. This also applies when you're refueling—always do that outside with the engine off.
It's a good practice to wear long pants and eye protection when mowing, and to clear the area of debris before you start.