“In Your Name, O Allah, I die and I live”
بِاسْمِكَ اللَّهُمَّ أَمُوتُ وَأَحْيَا
Bismika Allaahumma ‘amootu wa ‘ahyaa
Here, dying and living are metaphors for sleep and wakefulness. This explains why the normal order of these words has been reversed in this Hadith. In other contexts the living is mentioned before dying.
See Qur’an Al-Baqarah 2:258, Aal-‘Imrdn 3:156, Al-A’raf 7:158 among many other examples. See also Al-Asqalani, Fathul-Bari 11/113, Muslim 4/ 2083.