  A mixed graph is a graph with undirected and directed edges. Guo and Mohar in
2017 determined all mixed graphs whose Hermitian spectral radii are less than
$2$. In this paper, we give a sufficient condition which can make Hermitian
spectral radius of a connected mixed graph strictly decreasing when an edge or
a vertex is deleted, and characterize all mixed graphs with Hermitian spectral
radii at most $2$ and with no cycle of length $4$ in their underlying graphs.
