Activating　closed　natural　fractures　(NFs)　in　hot　dry　rock　(HDR)　reservoirs　is　a　critical　way　to　improve　fluid　conductivity　and　stimulate　production.　However,　the　current　hydraulic　fracturing　simulation　technology　is　limited　in　its　ability　to　investigate　the　interaction　mechanism　between　hydraulic　fractures　(HFs)　and　NFs　under　the　interference　of　mineral　heterogeneity　in　HDR.　In　this　study,　we　combine　a　modified　hydro-grain-based　model　(hydro-GBM)　and　the　smooth　joint　model　(SJM)　to　establish　a　discrete　element　model　of　granite　with　closed　NFs,　investigating　the　effects　of　in-situ　stress,　approach　angle,　and　physico-mechanical　properties　of　NFs　on　interaction　modes.　Our　results　show　that　mineral　heterogeneity　induces　HFs　on　both　sides　of　the　borehole　to　propagate　asymmetrically　along　low-strength　minerals　and　mineral　boundaries,　enhancing　the　complexity　of　HFs.　As　the　approach　angle,　NF　interface　friction　coefficient,　or　NF　bond　strengths　decrease　and　differential　in-situ　stress　or　NF　permeability　increases,　the　offset　of　HFs　propagating　along　NFs　increases,　thus　promoting　the　activation　degree　of　NFs　and　resulting　in　a　decline　in　the　average　activity　level　of　acoustic　emission　(AE)　events　and　the　proportion　of　large　events　in　NFs.　Furthermore,　numerical　simulations　reveal　the　evolution　laws　of　fracturing　results,　such　as　breakdown　pressure,　fracture　propagation　pressure,　spatial　distribution　of　microcracks,　fluid　pressure　field,　and　normal　stresses　on　NFs,　which　provide　valuable　insights　for　constructing　complex　and　efficient　fracture　networks　in　HDR　reservoirs.　A　smooth　joint　coupling　hydro-grain-based　model　is　proposed　to　describe　the　crystalline　rock　with　closed　natural　fractures　from　the　mineral　grain　scale.The　model　reproduces　the　interaction　modes　between　hydraulic　fractures　and　natural　fractures　similar　to　the　experimental　results.Effects　of　in-situ　stress,　approach　angle,　and　physico-mechanical　properties　of　natural　fractures　on　interaction　processes　are　deeply　analyzed.Evolution　laws　of　normal　stresses　and　AE　responses　for　natural　fractures　during　interactions　are　revealed.