  In this work, we study the long-standing experimental anomaly in muon $(g-2)$
and also recent anomalous excess in $K_L\to \pi^0+\nu\bar\nu$ at the J-PARC
KOTO experiment with sgoldstino. After supersymmetry breaking, the interactions
between quarks and sgoldstino ($s$) make the decays $K\to \pi+s$ sizable
through loop diagrams, which affects the measurements of decays $K\to
\pi+\mathrm{invisible}$. Furthermore, the couplings between photons and
sgoldstino contribute to $\Delta a_\mu$ as well as the bino-slepton
contribution. With satisfying all known experimental constraints such as from
NA62, E949, E137, Orsay, KTEV and CHARM experiments, these two anomalies can be
explained simultaneously. The mass of CP-even sgoldstino is close to the
neutral pion mass which does not violate the Grossman-Nir bound. The parameter
space can be further tested in future NA62, DUNE experiments, as well as
experiments in the LHC.
