Planet-planet scattering is the best candidate mechanism for explaining the eccentricity distribution of exoplanets. Here we study the survival and dynamics of exomoons under strong perturbations during giant planet scattering. During close encounters, planets and moons exchange orbital angular momentum and energy. The most common outcomes are the destruction of moons by ejection from the system, collision with the planets and the star, and scattering of moons onto perturbed but still planet-bound orbits. A small percentage of interesting moons can remain bound to ejected (free-floating) planets or be captured by a different planet. Moons' survival rate is correlated with planet observables such as mass, semi-major axis, eccentricity and inclination, as well as the close encounter distance and the number of close encounters. In addition, moons' survival rate and dynamical outcomes are predetermined by the moons' initial semi-major axes. The survival rate drops quickly as moons' distances increase, but simulations predict a good chance of survival for the Galilean moons. Moons with different dynamical outcomes occupy different regions of orbital parameter space, which may enable the study of moons' past evolution. Potential effects of planet obliquity evolution caused by close encounters on the satellites’ stability and dynamics will be reported, as well as detailed and systematic studies of individual close encounter events.