We describe the quasistatic and dynamic response of helical carbon nanotube (HCNT) foams in compression. Similarly to other CNT foams, HCNT foams exhibit preconditioning effects in response to cyclic loading; however, their fundamental deformation mechanisms are unique. In quasistatic compression, HCNT foams exhibit strain localization and collective structural buckling, nucleating at different weak sections throughout their thickness. In dynamic compression, they undergo progressive crushing, governed by the intrinsic density gradient along the thickness of the sample. HCNT microbundles often undergo brittle fracture that originates from nanoscale defects. Regardless of this microstructural damage, bulk HCNT foams exhibit super-compressibility and recover more than 90% of large compressive strains (up to 80%). When subjected to striker impacts, HCNT foams mitigate impact stresses more effectively compared to other CNT foams comprised of non-helical CNTs (similar to 50% improvement). The unique mechanical properties we revealed demonstrate that the HCNT foams are ideally suited for applications in packaging, impact protection, and vibration mitigation.