4.31

यज्ञशिष्टामृतभुजो यान्ति ब्रह्म सनातनम् ।
नायं लोकोऽस्त्ययज्ञस्य कुतोऽन्यः कुरुसत्तम ॥

yajñaśiṣṭāmṛtabhujo yānti brahma sanātanam
nāyaṃ loko 'sty ayajñasya kuto 'nyaḥ kurusattama

Kṛṣṇa (कृष्ण) is still speaking, to Arjuna.

The verse

Eaters of the nectar left from the sacrifice go to the eternal Brahman; this world is not for the one without sacrifice, how then another, best of the Kurus?

नेपालीमा

यज्ञबाट बचेको अमृत खानेहरू सनातन ब्रह्ममा जान्छन्। यज्ञ नभएकाका लागि यो लोक नै छैन भने अर्को लोक कसरी होला, हे कुरुहरूमा श्रेष्ठ?

Where it sits

4.30 said the stains are worn down, and this verse says the end of that is Brahman (ब्रह्म), while the one who sacrifices nothing has not this world and so not another. The list is about to be closed and ranked.

Split: यज्ञ-शिष्ट-अमृत-भुजः + यान्ति + ब्रह्म + सनातनम् + न + अयम् + लोकः + अस्ति + अयज्ञस्य + कुतः + अन्यः + कुरु-सत्तम

yajña-śiṣṭa-amṛta-bhujaḥ + yānti + brahma + sanātanam + na + ayam + lokaḥ + asti + ayajñasya + kutaḥ + anyaḥ + kuru-sattama

Sanskrit, in depth

The words

देवनागरीWordGrammarSense
यज्ञ-शिष्ट-अमृत-भुजःyajña-śiṣṭa-amṛta-bhujaḥnominative pluraleaters of the nectar that is the remainder of the sacrifice. śiṣṭa (शिष्ट) is "left." amṛta (अमृत) is the deathless, the nectar. bhuj (भुज्) at the end is "an eater."
यान्तिyāntipresent, 3rd pluralthey go. From yā (या).
ब्रह्मbrahmaaccusativeBrahman.
सनातनम्sanātanamaccusativeeternal. Agrees with brahma (ब्रह्म).
नnaindeclinablenot.
अयम्ayamnominativethis.
लोकःlokaḥnominativeworld.
अस्तिastipresent, 3rd singularis.
अयज्ञस्यayajñasyagenitiveof the one who has no sacrifice.
कुतःkutaḥindeclinablefrom where, how.
अन्यःanyaḥnominativeanother. Another world, after ayam lokaḥ (अयम् लोकः).
कुरु-सत्तमkuru-sattamavocativebest of the Kurus. sattama (सत्तम) is the superlative, "best."

The phrases

yajñaśiṣṭāmṛtabhujaḥ yānti brahma sanātanam (यज्ञशिष्टामृतभुजः यान्ति ब्रह्म सनातनम्) is where the sacrificers of 4.30 go. The eaters of the nectar left from the sacrifice go to the eternal Brahman. bhujaḥ yānti (भुजः यान्ति) is bhujo yānti (भुजो यान्ति).

na ayam lokaḥ asti ayajñasya (न अयम् लोकः अस्ति अयज्ञस्य) is who is left out. This world is not for the one who has no sacrifice. na ayam (न अयम्) is nāyam (नायम्). lokaḥ asti (लोकः अस्ति) is loko 'sti (लोकोऽस्ति), and asti ayajñasya (अस्ति अयज्ञस्य) is asty ayajñasya (अस्त्ययज्ञस्य). The whole run is loko 'sty ayajñasya (लोकोऽस्त्ययज्ञस्य).

kutaḥ anyaḥ kurusattama (कुतः अन्यः कुरुसत्तम) finishes the exclusion. How, then, another world? kutaḥ anyaḥ (कुतः अन्यः) is kuto 'nyaḥ (कुतोऽन्यः). The vocative faces Arjuna.

Sanskrit in this line

loko 'sty ayajñasya (लोकोऽस्त्ययज्ञस्य) is लोकः + अस्ति + अयज्ञस्य lokaḥ + asti + ayajñasya. First अः + अ aḥ + a becomes o (ओ) and drops the a (अ) of asti (अस्ति): loko 'sti (लोकोऽस्ति). Then इ + अ i + a joins asti (अस्ति) to ayajñasya (अयज्ञस्य): asty ayajñasya (अस्त्ययज्ञस्य). The genitive ayajñasya (अयज्ञस्य) is the person for whom the world "is not." It is not the subject. lokaḥ (लोकः) is the subject of asti (अस्ति).

Say it back

Who goes to Brahman, and for whom this world is not. If ayajñasya (अयज्ञस्य) is recited as yajñasya (यज्ञस्य), you have lost the negative. Stay here.