  We study two related universal anomalies of the spectral function of
cuprates, so called waterfall and high-energy kink features, by a combined
cellular dynamical mean-field theory and angle-resolved photoemission study for
the oxychloride Na$_x$Ca$_{2-x}$CuO$_2$Cl$_2$ (Na-CCOC). Tracing their origin
back to an interplay of spin-polaron and local correlation effects both in
undoped and hole-doped (Na-)CCOC, we establish them as a universal crossover
between regions differing in the momentum dependence of the coupling and not
necessarily in the related quasiparticles' energies. The proposed scenario
extends to doping levels coinciding with the cuprate's superconducting dome and
motivates further investigations of the fate of spin-polarons in the
superconducting phase.
