Oh em gee that is fantastic. I'm getting ziljan
2 hours of sleep last night so too tired to do a fully detailed explanation. But yes indeed the tidal forces would be more than enough to rip apart this M class star apart. If the Neutron was also a Pulsar (spinning neutron star) then it would look something like this:
[video=youtube;GI-TfRqy8Ts]https://www.youtube.com/watch?v=GI-TfRqy8Ts[/video]
One interesting question is how did they get so close in the first place? The formation of a neutron star is a violent (supernova!) process, and would have dramatically altered the orbit and mass of M star (which may have initially been a K, G or higher star). For instance this process can eject loosely bound stars and planets from the system. However, there are lots of reasons an orbit can degrade, especially in a chaotic multiple star system. This one is a bit of a head scratcher, especially on 2 hours of sleep!

One possible reason is that the planetary nebula from one (or both) of the NS formations caused the inner part of the system to lose angular momentum (like spreading out your arms while spinning on a chair). Another could be an interaction between the magnetic fields of the neutron star and the M star caused drag that degraded their orbits. Yet another explanation is that the creation of the outer Neutron destabilized the M star's higher orbit and sent it careening into the the other NS.