  In this paper, we generalize the work of the second author and prove a
grading shifting property, in sutured monopole and instanton Floer theories,
for general balanced sutured manifolds. This result has a few consequences.
First, we offer an algorithm that computes the Floer homologies of a family of
sutured handle-bodies. Second, we obtain a canonical decomposition of sutured
monopole and instanton Floer homologies and build polytopes for these two
theories, which was initially achieved by Juh\'asz for sutured (Heegaard) Floer
homology. Third, we establish a Thurston-norm detection result for monopole and
instanton knot Floer homologies, which were introduced by Kronheimer and
Mrowka. The same result was originally proved by Ozsv\'ath and Szab\'o for link
Floer homology. Last, we generalize the construction of minus versions of
monopole and instanton knot Floer homology, which was initially done for knots
by the second author, to the case of links. Along with the construction of
polytopes, we also proved that, for a balanced sutured manifold with vanishing
second homology, the rank of the sutured monopole or instanton Floer homology
bounds the depth of the balanced sutured manifold. As a corollary, we obtain an
independent proof that monopole and instanton knot Floer homologies, as
mentioned above, both detect fibred knots in $S^3$. This result was originally
achieved by Kronheimer and Mrowka.
