We present an analysis of the X-ray cluster morphologies of six z ~ 1 galaxy clusters from the Massive and Distant Clusters of WISE Survey (MaDCoWS). MaDCoWS is dedicated to identifying the most massive, stellar mass-selected galaxy clusters at 0.7 < z < 1.5 over the full extragalactic sky based upon data from the Wide-field Infrared Survey Explorer (WISE ) mission (Gonzalez et al. 2019). Since X-ray images are capable of detecting distinctive features of cluster morphology, like cool-cores and departures from axial symmetry, we use Chandra images to morphologically classify a sample of six MaDCoWS clusters. In this study, we choose photon asymmetry (Aphot ), developed by Nurgaliev et al. (2013), as the substructure statistic. We picked Aphot over other conventional asymmetry parameters since it is a robust, unbiased quantitative measure of the degree of the cluster disturbance for observations that suffer from low photon counts, high redshift, and a wide range of signal-to-noise ratios. Our cluster classification based on this parameter is in good agreement with by-eye classification. The scope of this study is not limited to separating galaxy clusters into relaxed and non-relaxed categories, but to exploit the correlations between the dynamical state of the galaxy clusters and the X-ray gas properties of the intracluster medium (ICM), as well as the role of active galactic nucleus (AGN) feedback. The overall goal is to gain new insights into the physical processes governing cluster evolution and merging histories.