Concurrent climate extremes in major crop-producing regions, such as synchronised droughts or heatwaves, threaten food security by causing simultaneous harvest failures. Such multi-breadbasket failures disrupt global food trade, particularly affecting import-dependent countries. While the probability and drivers of multi-breadbasket failures have previously been studied, the effects on importing countries via agricultural trade are less clear. Here, we combine national agricultural statistics, bilateral trade information, and historical climate data to quantify how simultaneous heatwaves or droughts impact global wheat production and exports. We find that concurrent heatwaves in major wheat producers significantly reduce production and exports, particularly in predominantly rainfed countries. Country-specific analyses reveal that production in key trade partners of most wheat-importing countries is highly sensitive to both heatwaves and droughts, however impacts on imports and domestic supply are more varied. Using a composite risk index, we highlight individual vulnerabilities of wheat-importing countries to production shocks due to compounding extremes.