The　interplay　between　traffic　dynamics　and　epidemic　spreading　on　complex　networks　has　received　increasing　attention　in　recent　years.　However,　the　control　of　traffic-driven　epidemic　spreading　remains　to　be　a　challenging　problem.　In　this　Brief　Report,　we　propose　a　method　to　suppress　traffic-driven　epidemic　outbreak　by　properly　removing　some　edges　in　a　network.　We　find　that　the　epidemic　threshold　can　be　enhanced　by　the　targeted　cutting　of　links　among　large-degree　nodes　or　edges　with　the　largest　algorithmic　betweenness.　In　contrast,　the　epidemic　threshold　will　be　reduced　by　the　random　edge　removal.　These　findings　are　robust　with　respect　to　traffic-flow　conditions,　network　structures,　and　routing　strategies.　Moreover,　we　find　that　the　shutdown　of　targeted　edges　can　effectively　release　traffic　load　passing　through　large-degree　nodes,　rendering　a　relatively　low　probability　of　infection　to　these　nodes.