Experimental research has shown that the incorporation of nanosilica (NS) filler in carbon/epoxy (c/ep) cylindrical tubes decreases the damaged area and increases the residual torsional strength of following normal incidence ballistic impact. The current investigation aims to determine the effect of NS on the residual torsional strength (RTS) of c/ep cylindrical tubes subjected to a static torsional load during oblique-incidence ballistic impact, where the projectile grazes the outer radius of the tube at a 45° angle in order to remove the largest amount of material (slashing impact). A total of four tubes were evaluated—two with 15% NS as a percent of matrix weight and two without NS filler. One of the impact tests resulted in two distinct holes in the tube rather than an elliptical gouged-out area, resulting in a reduced overall damage area and less degraded RTS versus the properly impacted tubes. The RTS retention of the three tubes having the intended impact trajectory was approximately 12% of the estimated strength of undamaged tubes. Likewise, the size of the damage zone surrounding the impact site, determined by coin-tapping, was also similar among the properly impacted tubes. Overall, the results are comparable with previously published slashing impact data for carbon fiber composite tubes made with various matrix materials and highlight the dominant influence of fiber damage versus matrix damage on the RTS of composite tubes following slashing ballistic impact.