A Trial to Evaluate Safety and Efficacy of Elamipretide Primary Mitochondrial Myopathy Followed by Open-Label Extension

PART 1: Inclusion Criteria: * Willing and able to provide a signed informed consent form prior to participation in any trial-related procedures * Agrees to adhere to the trial requirements for the length of the trial, including the use of the elamipretide delivery system * Subject is ≥ 16 and ≤ 80 years of age * Diagnosed with PMM in the opinion of the investigator and confirmed by an Adjudication Committee * Woman of childbearing potential must agree to use a highly effective method of birth control Exclusion Criteria: * Subject has myopathic signs and or/symptoms due to a neuropathic process or gait problem that would interfere with the 6 minute walk test (6MWT), in the opinion of the Investigator * Female who are pregnant, planning to become pregnant, or breastfeeding/lactating * At Screening, the estimated glomerular filtration rate (eGFR) \< 30 mL/min/1.73 m\^2 * Subject has undergone an in-patient hospitalization within the 30 days prior to the Baseline Visit or has a planned hospitalization or a surgical procedure during the trial. * Subject has clinically significant cardiac disease or prior interventional procedure and/or respiratory disease (medical history or current clinical findings) within 3 months of the Baseline Visit, in the opinion of the Investigator. * Subject has QTc elongation (using the correction factor utilized at the clinical site) defined as a QTc \>450 msec in male subjects and \>480 msec in female subjects. * ECG evidence of acute ischemia, atrial fibrillation, or active conduction system abnormalities with the exception of any of the following: 1. First degree Atrioventricular bock (AV-block) 2. Second degree AV-block Type 1 (Mobitz Type 1 / Wenckebach type) 3. Right bundle branch block * Subject has severe vision impairment that, in the opinion of the Investigator, may interfere with their ability to complete all trial requirements * Subject has a seizure disorder that, in the opinion of the Investigator, may interfere with their ability to complete all trial requirements. * Active malignancy or any other cancer from which the subject has been disease-free for \< 2 years. * Subject has a solid organ transplant and/or is currently receiving treatment with therapy for immunosuppression, in the opinion of the Investigator. * Subject has been previously diagnosed with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C infection. * Subject has a history of a systemic eosinophilic illness and/or an eosinophil count \>1,000 cells x10\^6/L at the Screening Visit. * Subject is currently participating or has participated in an interventional clinical trial (i.e.,investigational product or device, stem cell therapy, gene therapy) within 30 days of the Baseline Visit; or is currently enrolled in a non-interventional clinical trial (except for SPIMM-300) at the Baseline Visit which, in the opinion of the Investigator, may be potentially confounding with results of the current trial (e.g., exercise therapy trial). * Subject has previously received elamipretide (MTP-131), for any reason. * Subject has a history of active substance abuse during the year before the Baseline Visit, in the opinion of the Investigator. * Subject has any prior or current medical condition that, in the judgment of the Investigator, would prevent the subject from safely participating in and/or completing all trial requirements. PART 2: Continuation Criteria: * Subjects must continue to be able and willing to adhere to the trial requirements. * Subject is appropriate to continue in Part 2 (i.e. subject was compliant in Part 1), in the opinion of the Investigator. * Subject has not had a serious adverse event (SAE)/serious adverse device effect (SADE) attributed to the elamipretide delivery system. * Subject has not permanently discontinued the elamipretide delivery system.