  Layered van der Waals (vdW) magnets are prominent playgrounds for developing
magnetoelectric, magneto-optic and spintronic devices. In spintronics,
particularly in spincaloritronic applications, low thermal conductivity
($\kappa$) is highly desired. Here, by combining thermal transport measurements
with density functional theory calculations, we demonstrate low $\kappa$ down
to 1 W m$^{-1}$ K$^{-1}$ in a typical vdW ferromagnet Cr$_2$Si$_2$Te$_6$. In
the paramagnetic state, development of magnetic fluctuations way above
$T_\mathrm{c}=$ 33 K strongly reduces $\kappa$ via spin-phonon scattering,
leading to low $\kappa \sim$ 1 W m$^{-1}$ K$^{-1}$ over a wide temperature
range, in comparable to that of amorphous silica. In the magnetically ordered
state, emergence of resonant magnon-phonon scattering limits $\kappa$ below
$\sim$ 2 W m$^{-1}$ K$^{-1}$, which would be three times larger if magnetic
scatterings were absent. Application of magnetic fields strongly suppresses the
spin-phonon scattering, giving rise to large enhancements of $\kappa$. Our
calculations well capture these complex behaviours of $\kappa$ by taking the
temperature- and magnetic-field-dependent spin-phonon scattering into account.
Realization of low $\kappa$ which is easily tunable by magnetic fields in
Cr$_2$Si$_2$Te$_6$, may further promote spincaloritronic applications of vdW
magnets. Our theoretical approach may also provide a generic understanding of
spin-phonon scattering, which appears to play important roles in various
systems.
