Final answer:
The pectoralis minor was the partially severed muscle encountered during surgery to repair a severed artery in the axilla following a stab wound.
Step-by-step explanation:
The muscle that was partially severed and runs downward and medially from the coracoid process is the pectoralis minor. This muscle stabilizes the scapula by drawing it anteriorly and downward against the thoracic wall. It originates from the anterior surface of the third to fifth ribs and inserts on the coracoid process of the scapula. During the surgical procedure described, after dividing the clavicular head of the pectoralis major muscle and retracting it, the exposure of a bloody fat-filled space indicates entry into the axilla, where the important vessels and nerves for the upper limb are located, including the axillary artery which was presumably the severed vessel.