  In this paper, we give presentations of the mapping class groups of marked
surfaces stabilizing boundaries for any genus. Note that in the existing works,
the mapping class groups of marked surfaces were the isotopy classes of
homeomorphisms fixing boundaries pointwise. The condition for stabilizing
boundaries of mapping class groups makes the requirement for mapping class
groups to fix boundaries pointwise to be unnecessary. As an application of
presentations of the mapping class groups of marked surfaces stabilizing
boundaries, we obtain the presentation of the cluster automorphism group of a
cluster algebra from a feasible surface $(S,M) $. Lastly, for the case (1)
4-punctured sphere, the cluster automorphism group of a cluster algebra from
the surface is characterized. Since cluster automorphism groups of cluster
algebras from those surfaces were given in \cite{ASS} in the cases (2) the
once-punctured 4-gon and (3) the twice-punctured digon, we indeed give
presentations of cluster automorphism groups of cluster algebras from surfaces
which are not feasible.
