In Greek, "breath" and "spirit" are the same word - πνευμα. εξεπνευσεν is composed of the two words, ἔξω (out) and πνεῦμα (breath/spirit). Thus εξεπνευσεν could mean "breathed out" or "released the spirit." Matthew 27:50 describes the same narrative, albeit with slightly different wording. It says: "ιησους... αφηκεν το πνευμα (Jesus... released the breath/spirit)." Interestingly, the NIV, ESV, and NASB all render this phrase as "Jesus... gave up his spirit." The KJV's rendering of Mark 15:37 maintains uniformity with the rendering in Matthew 27:50 in the KJV as well as in other translations.
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