Two of his older brothers died young, and the third (Date Murakaze) formed a separate hatamoto household, so he was appointed heir.
As was his father, he was noted for his literary achievements, and he was also proficient in horsemanship, swordsmanship, use of the spear, military strategy and hōjutsu (gunnery).
In 1747, Hosokawa Munetaka, daimyō of Kumamoto Domain was cut down by a hatamoto, Itakura Katsukane, while en route to a ceremony at Edo Castle.
Date Munemura, who happened to be nearby when the incident occurred, knelt by the corpse of Hosokawa Munetake and loudly declared "he still lives!"
and ordered his retainers to take the body to the Hosokawa clan residence before the Shogun's metsuke inspectors could arrive at the scene.