  Debris discs consist of belts of bodies ranging in size from dust grains to
planetesimals; these belts are visible markers of planetary systems around
other stars that can reveal the influence of extrasolar planets through their
shape and structure. Two key stirring mechanisms -- self-stirring by
planetesimals and secular perturbation by an external giant planet -- have been
identified to explain the dynamics of planetesimal belts; their relative
importance has been studied independently, but are yet to be considered in
combination. In this work we perform a suite of 286 N-body simulations
exploring the evolution of debris discs over 1~Gyr, combining the gravitational
perturbations of both dwarf planets embedded in the discs, and an interior
giant planet. Our systems were somewhat modeled after the architecture of the
outer Solar system: a Solar mass star, a single massive giant planet at 30~au
($M_{\rm GP} =$ 10 to 316~$\mathrm{M}_{\oplus}$), and a debris disc formed by
100 massive dwarf planets and 1000 massless particles ($M_{\rm DD} =$ 3.16 to
31.6~$\mathrm{M}_{\oplus}$). We present the evolution of both the disc and the
giant planet after 1~Gyr. The time evolution of the average eccentricity and
inclination of the disc is strongly dependent on the giant planet mass as well
as on the remaining disc mass. We also found that efficient stirring is
achieved even with small disc masses. In general, we find that a mixed
mechanism is more efficient in the stirring of cold debris discs than either
mechanism acting in isolation.
