The handle of this exquisitely carved Phurpa/chopper has partially a peacock's head with its ear and eyebrows made in the shape of a bird's wings. A chopper with bent tip is coming out from the mouth of a makara. There are four heads of Mahakala and two heads of Ganesha, arranged in vertical rows. On the top there is one head of Mahakala who is wearing a crown of skulls and has upswept hair, behind the crown. After this, there are two rows of the heads of Mahakala and Ganesha and in each row there are two heads are differently sized and shaped. All the heads of Mahakala has ferocious expressions with open mouth and bared fangs. They have three eyes, their beard is made of hook like shape, and they wear crown with skull ornaments. There are snakes around their necks. The well-polished heads of Ganesha are also wearing crown and have three eyes along with their trunks and Turks.
So, far as the association of Ganesha with the Mahakala is concerned, it is well know that Ganesha was also incorporated into Buddhist pantheon, particularly in Japan, and it is said that Mahakala is prototype of Siva-Maheshvara. Ganesha is the son of Siva and Parvati, and thus the association of Ganesha with Mahakala seems natural and we may consider it as a composite from of both the deities. But it is also notable that there is numerous representation of Mahakala where he is trampling Ganesha. The present representation is perhaps artist's creation where both the deities have been shown in a composite form.
A.K.Gordon, The Iconography of Tibetan Lamaism, New York, 1939
A.Getty, The Gods of Northern Buddhism, Tokyo, 1962
A.Waddel, Buddhism and Lamaism, of Tibet, Delhi, 1978 (reprint)
D.N.Bakshi, Hindu Divinities in Japanese Buddhist Pantheon, Calcutta, 1979
Wrathful Guardian of Buddhism: Aesthetics and mythology, Article of the month Feb.2001, Exotic India.
This description by Dr. Shailendra Kumar Verma, Ph.D. His doctorate thesis being on the "Emergence and Evolution of the Buddha Image (from its inception to 8th century A.D).
Of Related Interest :
Ritual Implements in Tibetan Buddhism: A Symbolic Appraisal