We study the Globular Cluster (GC) system of the nearby elliptical galaxy M87 using the newly available dataset with accurate kinematics provided by Strader et al. (2011). We find evidence for three distinct sub-populations of GCs in terms of colours, kinematics and radial profiles. We show that a decomposition into three populations -blue, intermediate and red GCs -is statistically preferred to one with two or four populations. The existence of three components has been suggested before, but here we are able to identify them robustly and relate them to the stellar profile. We exploit the sub-populations to derive dynamical constraints on the mass and Dark Matter (DM) content of M87 out to ∼ 100 kpc. We deploy a class of global mass-estimators, developed in Paper I, obtaining mass measurements at different locations. The DM fraction in M87 changes from ≈0.2 at the effective radius of the stellar light (0.02• or 6 kpc) to ≈0.95 at the distance probed by the most extended, blue GCs (0.47• or 135 kpc).We supplement this analysis with virial decompositions, which exploit the dynamical model to produce a separation into multiple components. These yield the luminous mass as 5.511 M ⊙ and the dark matter within 135 kpc as 8.0The inner DM density behaves as ρ ∼ r −γ with γ ≈ 1.6. This is steeper than the cosmologically preferred cusp of ρ ∼ r −1 (Dubinski & Carlberg; Navarro, Frenk & White), and may provide evidence of dark matter contraction. Finally, we combine the GC separation into three sub-populations with the Jeans equations, obtaining information on the orbital structure of the GC system. The centrally concentrated red GCs exhibit tangential anisotropy, consistent with the depletion of radial orbits by tidal shredding. The most extended blue GCs have an isotropic velocity dispersion tensor in the central parts, which becomes more tangential moving outwards, consistent with adiabatic contraction of the DM halo.