Díaz signed with the Minnesota Twins as an international free agent on November 21, 2013. He played for the DSL Twins in 2014, hitting .257/.385/.451/.836 with 5 home runs and 27 RBI. He split the 2015 season between the GCL Twins and the Elizabethton Twins, hitting a combined .233/.322/.371/.693 with 4 home runs and 20 RBI. He returned to Elizabethton in 2016, and hit .310/.353/.575/.928 with 9 home runs and 37 RBI. He played for the Cedar Rapids Kernels in 2017, hitting .292/.329/.444/.773 with 12 home runs and 68 RBI. He spent the 2018 season with the Fort Myers Miracle, hitting .224/.255/.344/.599 with 6 home runs and 38 RBI. He opened the 2019 season back with Fort Myers, before being promoted to the Pensacola Blue Wahoos on June 19. Between the two teams, he hit a combined .294/.336/.553/.889 with 19 home runs and 62 RBI.
