Can the Mini be serviced by most garages that work on sports cars?
Sure. Even some garages that work on large sedans and small econo-boxes. Why do you think it cannot?
Mini’s can be serviced by any decent independent garage with exposure to European cars.
Heck, it can be serviced by most garages, even those not specializing in sports cars.
Ditto to what has already been stated, but I want to add that it is VERY important to ensure that a service facility other than the dealership is using the correct specification (European) motor oil.
Many independents don’t stock that type of oil and using ordinary old US-spec oil is a sure way to ruin that engine–especially if you use the absurdly long oil change intervals specified by BMW for their Mini vehicles.
What type of service are you talking about?
Simple engine oil change? Yes, but as mentioned, make sure they use the proper spec engine oil for the car (read the owners manual to find out what it needs).
For a transmission fluid change?
Possibly not, especially if it has a CVT transmission.
This transmission needs a special fluid, and should never be “flushed”, just drain and refill. A manual transmission can be serviced by any shop, however.
Yup, any place that can change tires can do them on the Mini.
That’s the normal stuff.
Anything outside of that list, you are going to have to specify.