The purpose of this study is to evaluate the effects of RM-131 on gastric emptying, gastroparesis symptoms, and the safety and tolerability of RM-131 compared to placebo in patients with Type 1 and Type 2 diabetes mellitus and gastroparesis. The study is designed to evaluate the efficacy and safety of multiple dose regimens of RM-131. Study drug (RM-131 and placebo) will be administered subcutaneously in a blinded fashion.