SB 3.16.6

yasyāmṛtāmala-yaśaḥ-śravaṇāvagāhaḥ
 sadyaḥ punāti jagad āśvapacād vikuṇṭhaḥ
so ’haṁ bhavadbhya upalabdha-sutīrtha-kīrtiś
 chindyāṁ sva-bāhum api vaḥ pratikūla-vṛttim
Synonyms: 
yasya — of whom; amṛta — nectar; amala — uncontaminated; yaśaḥ — glories; śravaṇa — hearing; avagāhaḥ — entering into; sadyaḥ — immediately; punāti — purifies; jagat — the universe; āśva-pacāt — including even the dog-eaters; vikuṇṭhaḥ — without anxiety; saḥ — that person; aham — I am; bhavadbhyaḥ — from you; upalabdha — obtained; su-tīrtha — the best place of pilgrimage; kīrtiḥ — the fame; chindyām — would cut off; sva-bāhum — My own arm; api — even; vaḥ — towards you; pratikūla-vṛttim — acting inimically.
Translation: 
Anyone in the entire world, even down to the caṇḍāla, who lives by cooking and eating the flesh of the dog, is immediately purified if he takes bath in hearing through the ear the glorification of My name, fame, etc. Now you have realized Me without doubt; therefore I will not hesitate to lop off My own arm if its conduct is found hostile to you.
Purport: 

Real purification can take place in human society if its members take to Kṛṣṇa consciousness. This is clearly stated in all Vedic literature. Anyone who takes to Kṛṣṇa consciousness in all sincerity, even if he is not very advanced in good behavior, is purified. A devotee can be recruited from any section of human society, although it is not expected that everyone in all segments of society is well-behaved. As stated in this verse and in many places in Bhagavad-gītā, even if one is not born in a brāhmaṇa family, or even if he is born in a family of caṇḍālas, if he simply takes to Kṛṣṇa consciousness he is immediately purified. In Bhagavad-gītā, Ninth Chapter, verses 30-32, it is clearly stated that even though a man is not well-behaved, if he simply takes to Kṛṣṇa consciousness he is understood to be a saintly person. As long as a person is in this material world he has two different relationships in his dealings with others — one relationship pertains to the body, and the other pertains to the spirit. As far as bodily affairs or social activities are concerned, although a person is purified on the spiritual platform, it is sometimes seen that he acts in terms of his bodily relationships. If a devotee born in the family of a caṇḍāla (the lowest caste) is sometimes found engaged in his habitual activities, he is not to be considered a caṇḍāla. In other words, a Vaiṣṇava should not be evaluated in terms of his body. The śāstra states that no one should think the Deity in the temple to be made of wood or stone, and no one should think that a person coming from a lower-caste family who has taken to Kṛṣṇa consciousness is still of the same low caste. These attitudes are forbidden because anyone who takes to Kṛṣṇa consciousness is understood to be fully purified. He is at least engaged in the process of purification, and if he sticks to the principle of Kṛṣṇa consciousness he will very soon be fully purified. The conclusion is that if one takes to Kṛṣṇa consciousness with all seriousness, he is to be understood as already purified, and Kṛṣṇa is ready to give him protection by all means. The Lord assures herein that He is ready to give protection to His devotee even if there is need to cut off part of His own body.