The mystery of the sannyāsa-daṇḍa (staff) of Śrī Caitanya Mahāprabhu has been explained by Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura. Śrī CaitanyaMahāprabhu accepted the order of sannyāsa from a Māyāvādī sannyāsī. The Māyāvādī sannyāsīs generally carry one staff, or daṇḍa. Taking advantage of Śrī Caitanya Mahāprabhu's absence, Śrīla Nityānanda Prabhu broke the staff into three parts and threw it into the river later known as the Daṇḍa-bhāṅgā-nadī. In the sannyāsa order there are four divisions—kuṭīcaka, bahūdaka, haṁsa and paramahaṁsa. Only when the sannyāsī remains on the kuṭīcaka and bahūdaka platforms can he carry a staff. However, when one is elevated to the status of haṁsa or paramahaṁsa, after touring and preaching the bhakti cult, he must give up the sannyāsa staff.
(Sri Caitanya Caritamrta------2:5:142-143-----purport).

Śrī Nityānanda Prabhu considered Lord Caitanya Mahāprabhu's acceptance of sannyāsa to be useless. He therefore relieved the Lord of the trouble of carrying the staff. Śrī Caitanya Mahāprabhu expressed anger because He wanted to teach all other sannyāsīs that they should not give up the staff before attaining the platform of paramahaṁsa. Seeing that the regulative principles could be slackened by such action, Caitanya Mahāprabhu wanted to carry the staff personally. However, Nityānanda broke it. For this reason Caitanya Mahāprabhu displayed a little anger. It is said in the Bhagavad-gītā (3.21), yad yad ācarati śreṣṭhas tat tad evetaro janaḥ: Whatever great people do, others follow. ŚrīCaitanya Mahāprabhu wanted to follow the Vedic principles strictly in order to save inexperienced neophytes who try to imitate paramahaṁsas.
(Sri Caitanya Caritamrta------2:5:152-----purport).

All the previous ācāryas, being induced to engage themselves fully in the service of the Lord, gave up attachment for material life and thus accepted the staff, which signifies full engagement of the mind, speech and body in the service of the Lord. Śrī Caitanya Mahāprabhu accepted the regulative principles of the renounced order of life. That is completely clear. However, in the paramahaṁsa stage there is no need to accept a daṇḍa (staff), and Śrī Caitanya Mahāprabhu was certainly in the paramahaṁsa stage. Nonetheless, to indicate that everyone should take sannyāsa at the end of life in order to engage fully in the service of the Lord, even paramahaṁsas like Śrī Caitanya Mahāprabhu and His confidential devotees follow the regulative principles unfailingly.
(Sri Caitanya Caritamrta------2:5:158-----purport).