ABSTRACT Several stars show deep transits consistent with discs of roughly $1\mathrm{\, R}_\odot$ seen at moderate inclinations, likely surrounding planets on eccentric orbits. We show that this configuration arises naturally as a result of planet–planet scattering when the planets possess satellite systems. Planet–planet scattering explains the orbital eccentricities of the discs’ host bodies, while the close encounters during scattering lead to the exchange of satellites between planets and/or their destabilization. This leads to collisions between satellites and their tidal disruption close to the planet. Both of these events lead to large quantities of debris being produced, which in time will settle into a disc such as those observed. The mass of debris required is comparable to a Ceres-sized satellite. Through N-body simulations of planets with clones of the Galilean satellite system undergoing scattering, we show that 90 per cent of planets undergoing scattering will possess debris from satellite destruction. Extrapolating to smaller numbers of satellites suggests that tens of per cent of such planets should still possess circumplanetary debris discs. The debris trails arising from these events are often tilted at tens of degrees to the planetary orbit, consistent with the inclinations of the observed discs. Disruption of satellite systems during scattering thus simultaneously explains the existence of debris, the tilt of the discs, and the eccentricity of the planets they orbit.