  We study the photoinduced dynamics of finite-momentum spin excitations in
two-dimensional Mott insulators on a square lattice. By calculating the
time-resolved resonant inelastic X-ray scattering (trRIXS) cross-section, we
show that an ultrafast pump above the Mott gap induces a prompt softening of
the spin excitation energy, compatible with a transient renormalization of the
exchange interaction. While spin fluctuations in a hole-doped system
(paramagnons) are well described by Floquet theory, magnons at half filling are
found to deviate from this picture. Furthermore, we show that the paramagnon
softening is accompanied by an ultrafast suppression of $d$-wave pairing
correlations, indicating a link between the transient spin excitation dynamics
and superconducting pairing far from equilibrium.
