What you are asking for is a classic task for learning pattern recognition, also known as the "chicken sexer problem" (derived from the people whose job at a farm is to throw recently-emerged chickens into one crate if female and another if male). The way to learn this is only one: practice. And not being able to taste is making it much harder.
Note that this is not a case where somebody could get you a description of how to recognize the difference and you could go through it and make checkmarks. Even people who succeed at the task will not be able to tell you how they know which it is (they may have a subjective explanation for it, such as "one of them smells faintly like a barn, the other doesn't", but it is not necessary true). The way to do it is to sit together with somebody who is adept at it, and watch their process intently over several hundred to thousand samples, until you realize you can tell the difference yourself. If there is no such expert available, the other way is to have those several hundred to thousand samples prepared by somebody who knows which is beef and which mutton, and you will have to start doing the process on your own, getting a correctness feedback after each sample. It will be slightly slower than sitting with an expert.
The task is likely to be rather context-dependent: you will probably have to go through a separate learning process for hot pot, and a separate one for Korean BBQ. The number of samples you need is also likely to be context-dependent, for example it is much easier to tell apart beef and mutton when grilled (there you will probably need less than one hundred samples) than when presented as salami.