This study investigates the combined impacts of the Madden-Julian oscillation (MJO) and extratropical anticyclonic Rossby wave breaking (AWB) on sub-seasonal Atlantic tropical cyclone (TC) activity and their physical connections. Our results show that during MJO phases 2-3 (enhanced Indian Ocean convection) and 6-7 (enhanced tropical Pacific convection), there are significant changes in basin-wide TC activity. The MJO and AWB collaborate to suppress basin-wide TC activity during phases 6-7 but not during phases 2-3. During phases 6-7, when AWB occurs, various TC metrics including hurricanes, accumulated cyclone energy and the rapid intensification probability decrease by ~50%-80%. Simultaneously, large-scale environmental variables, like vertical wind shear, precipitable water, and sea surface temperatures become extremely unfavorable for TC formation and strengthening, compared to periods characterized by suppressed AWB activity during the same MJO phases. Further investigation reveals that AWB events during phases 6-7 occur in concert with the development of a stronger anticyclone in the lower troposphere, which transports more dry, stable extratropical air equatorward, and drives enhanced tropical SST cooling. As a result, individual AWB events in phases 6-7 can disturb the development of surrounding TCs to a greater extent than their phases 2-3 counterparts. The influence of the MJO on AWB over the western subtropical Atlantic can be attributed to the modulation of the convectively-forced Rossby wave source over the tropical eastern Pacific. A significant number of Rossby waves initiated from this region during phases 5-6 propagate into the subtropical North Atlantic, preceding the occurrence of AWB events in phases 6-7.