Your Mugho is fine. Leave those roots alone and leave that mulch alone. As the mulch decomposes your roots will adapt to being exposed. I would continue to add a thin layer of mulch; 1" over those roots when remulching your landscape beds. What mulch are you using?
Adding too much mulch OVER roots that are already established is harmful. The plant keeps its roots at an optimum depth to protect its roots from heat and cold yet be able to suck up the moisture.
Let's say your Mugho Pine has the majority of its roots at 4" deep. Dumping 2" more on top means those roots are now 50% deeper and would be getting 50% of the water it was used to getting. Not good. Mughos are not a 'sensitive' plant. A Daphne would fit this example better than Mugho.
Your (non) problem is that the mugho is able to get its roots closer to the surface again. This is not a problem. Those roots are also called 'feeder roots' getting as close to the surface as possible to ensure getting water. These roots have grown into the correct level to get the water, to cut them out and take the mulch off now would cause major stress for your mugho.
Leave the mulch alone under your mugho. It will do no harm. If your mugho was an azalea or a Daphne, very shallow roots then the application of 2" more mulch might have killed your plant, not the Mugho.
Send a picture, please. When was the last time you fertilized with a balanced, boxed or bagged, fertilizer?