Performs the first committed step in the biosynthesis of isoprene-containing compounds such as sterols and terpenoids. Is specific for (R)-5-diphosphomevalonate (MVAPP). The catalytic efficiency with (R)-5-phosphomevalonate (MVAP) as substrate is 10000-fold lower than for MVAPP. (R)-5-diphosphomevalonate + ATP = ADP + CO2 + isopentenyl diphosphate + phosphate kcat is 3.2 sec(-1) with (R)-5-diphosphomevalonate as substrate. kcat is 0.034 sec(-1) with (R)-5-phosphomevalonate as substrate. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 3/3. Homodimer. Belongs to the diphosphomevalonate decarboxylase family.