Tesla Service does not repair tires. In some areas Tesla can arrange to loan you a wheel and tire for a few days until you can have your damaged tire repaired or replaced.
Tesla Roadside Assistance can be reached by phone. Roadside Assistance will contact a contracted vehicle towing service for your area. The tow service may have a loaner wheel and tire but can't be expected to have every size wheel and tire combination for the full lineup of Tesla vehicles.
You have to balance the cost of carrying a spare wheel and tire with the inconvenience of your travel plans being interrupted until a suitable replacement tire can be found.
At a minimum when taking a trip away from your home location bring a 12V tire inflation air pump and a tire plug kit. Consider purchasing the Modern Spare kit for your Tesla Vehicle.