  We address scatterings of spin waves off uncorrelated defects in
two-dimensional (2D) easy-axis antiferromagnet (AFM) insulators. Although an
onsite magnetic anisotropy leads gapped Goldstone modes, such that a long range
(AFM) order can be established in 2D, lattice imperfections tend to weaken, and
eventually destroy the magnetic ordering. Here, the impact of defects is
considered within two limits, single and multiple defects. Using Green's
function, we perform self consistent simulations to study magnon properties
such as density of states and lifetime of induced resonances. Our findings show
that repulsive defects decrease the magnon density of states while attractive
ones may enhance it. We provide a comprehensive analysis of how defects can
result in a reduction and even closing, the anisotropy induced gap, which
weakens the long range (AFM) order parameter in the 2D state. We conclude that
a small concentration of random defects can fill the gap of magnon spectrum.
