ʿAqartu is a first-person singular perfect from ʿaqara–yaʿqiru. The root has several uses, but in this passage it refers to slaughtering an animal. Al-ʿadhārā is the plural of ʿadhrāʾ, and maṭiyyah denotes a riding animal.
The prepositional phrase li-l-ʿadhārā indicates those for whose sake the act was done. Maṭiyyatī is the direct object, with a first-person possessive ending identifying the mount as the poet's own.
Translating ʿaqartu simply as “I injured” would weaken the connection to the next verse's meat-sharing scene. Context determines the intended sense.