I too have the same exact problem. I bought the Microsoft Surface Mouse back in April and the scroll wheel simply broke just today July 22nd.
It's definitely a hardware problem. Has nothing to do with the OS or software. The wheel is simply spinning smoothly and freely without vibration. For the wheel to work, there needs to be vibration feedback, but obviously there is none now.
There is no Microsoft support on this unfortunately. I tried to get device warranty on this, but without any luck. All Microsoft hardware gets 1 year limited warranty, but when I contacted them about this, they refused to replace mine for free.
For all future Surface Mouse customers, BE WARNED! Don't buy this product. It is defective and has no warranty.