The Dvaya Mantra consists of two sentences: the pūrva vākya ('Śrīman Nārāyaṇa caraṇau śaraṇaṃ prapadye') and the uttara vākya ('Śrīmate Nārāyaṇāya namaḥ'). While the former is the act of surrender — placing oneself at the feet of Śrīman Nārāyaṇa — the uttara vākya is the utterance of the soul's aspiration: to render eternal, loving service (kaiṅkarya) to the Lord and Śrī in Śrīvaikuṇṭha.
Piḷḷai Lokācārya's Mumukṣuppadi provides a profound analysis of each element of the uttara vākya. The dative case in 'Nārāyaṇāya' expresses that all service is offered to Bhagavān — not for the jīva's own gratification, not even for the pleasure of rendering service itself. The word 'namaḥ' — literally 'not mine' (na mama) — is the pivot of the entire sentence: it explicitly renounces mamakāra, the claim that the service I render is 'my' service, offered by 'me' for 'my' fulfillment. By this renunciation, even kaiṅkarya itself is purified and offered back to the Lord free from any trace of self-interest.
The presence of 'Śrīmate' at the beginning of the uttara vākya mirrors its presence in the pūrva vākya, emphasizing that Śrī is ever inseparable from Nārāyaṇa and that all kaiṅkarya is rendered in the presence of — and indeed mediated by — Her grace. The uttara vākya thus encapsulates the entire vision of mokṣa in Śrī Vaiṣṇavism: not a state of inert liberation, but an eternal, joyful relationship of loving service in the company of the Lord and His consort.