By their own sword, i.e. by their arms or valour. The light of thy countenance, i.e. thy favour, as the next words explain it; thy gracious and glorious presence, which went along with us.
Related Commentaries of Psalms 44:3
Psalms 44:3
3 For they got not the land in possession by their own sword, neither did their own arm save them: but thy right hand, and thine arm, and the light of thy countenance, because thou hadst a favour unto them.