We can't determine what's causing the dieback by viewing the photos. Sometimes laboratory analysis of affected branches is needed to do that.
However, based upon what we can see, the mugo might be showing the effects of Dothistroma needle blight. According experts at the University of Illinois, "Dothistroma causes banding and dieback of affected needles. The very new growth at the tip of the branch often stays green for several months."
In any case, whatever has damage the plant appears to be so advanced that recovery is unlikely. If you want a second opinion, please ask a certified arborist to assess the tree's health onsite and recommend a course of action. If you decide to do that the following information may be useful: