The CERN accelerator complex is undergoing an upgrade in order to meet the requirements of the High-Luminosity Large Hadron Collider (HL-LHC). One of the key needs is to increase the intensity of beams injected into the LHC from the current $1.15\ifmmode\times\else\texttimes\fi{}{10}^{11}$ to $2.3\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }{\mathrm{p}}^{+}/\mathrm{bunch}$. This requires a beam intensity at injection in the Super Proton Synchrotron (SPS), the last injector before the LHC, as high as $2.6\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }{\mathrm{p}}^{+}/\mathrm{bunch}$, given that a budget for losses of about 10% is included in the design. However, previous experience with high intensity beams suggests that the total amount of losses in the SPS can be even higher, causing an increased activation, faster aging, and consequent early failure of machine equipment, in addition to an increase in the requirements for preinjectors in order to still meet the HL-LHC target in spite of higher losses. In this paper, we propose a collimation system to be used with HL-LHC proton beams in the SPS in order to intercept and safely dispose of beam losses in ad hoc locations and therefore provide the machine with protection against activation and equipment aging. The design is based on a two-stage concept, where the primary stage intercepts particles that otherwise would be lost, and the secondary stage employing an absorber where lost particles are finally disposed of. Numerical simulations prove a cleaning efficiency of the proposed system of at least 80%, substantially reducing the spreading of particle losses around the machine. Furthermore, the performance of the collimation system has a low sensitivity to common machine errors, and the design is cost efficient, with minimal hardware changes.