  We present a study of $\gamma$-ray emission from the core-collapse supernova
remnant Cas~A in the energy range from 0.1GeV to 10TeV. We used 65 hours of
VERITAS data to cover 200 GeV - 10 TeV, and 10.8 years of \textit{Fermi}-LAT
data to cover 0.1-500 GeV. The spectral analysis of \textit{Fermi}-LAT data
shows a significant spectral curvature around $1.3 \pm 0.4_{stat}$ GeV that is
consistent with the expected spectrum from pion decay. Above this energy, the
joint spectrum from \textit{Fermi}-LAT and VERITAS deviates significantly from
a simple power-law, and is best described by a power-law with spectral index of
$2.17\pm 0.02_{stat}$ with a cut-off energy of $2.3 \pm 0.5_{stat}$ TeV. These
results, along with radio, X-ray and $\gamma$-ray data, are interpreted in the
context of leptonic and hadronic models. Assuming a one-zone model, we exclude
a purely leptonic scenario and conclude that proton acceleration up to at least
6 TeV is required to explain the observed $\gamma$-ray spectrum. From modeling
of the entire multi-wavelength spectrum, a minimum magnetic field inside the
remnant of $B_{\mathrm{min}}\approx150\,\mathrm{\mu G}$ is deduced.
