English Translation
Mother had a large lung hemorrhage and died.
夥しい喀血をする sounds very unnatural for two reasons.
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喀血で死にました is more natural than 喀血をして死にました because 喀血 (a noun) is a symptom, so saying 喀血をする in Japanese sounds like “to execute hemoptysis” in English, which is a bad collocation.
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夥しい can be used together with 喀血, but in this case, you cannot use ~をする.
I would propose the following alternative translations:
母は大量の喀血で亡くなりました。(たいりょうのかっけつでなくなりました)
母は夥しい量の喀血の末、亡くなりました。(おびただしいりょうのかっけつのすえ、…)
Besides, 喀血 means “coughing up blood”. But the English sentence says “lung hemorrhage”. “Hemorrhage” per se doesn’t always result in “coughing up” especially among patients who are already on a ventilator or under anesthesia.