DakshaYagnaharamurti is the form of Lord Shiva, in which he spoils the Yagnya performed by Daksha to insult him and abuse him. This episode is mentioned in one of the epics where Lord Shiva is about to marry Goddess Shakti.
In this incident Lord Shiva takes the form of Daksha Yagnaharamurti, rather the form of Veerabhadra, which is his own form of anger. Dakshayani is the incarnation of Goddess Shakti, desiring to marry Lord Shiva.
Lord Shiva is turning to his ferocious form to destroy Daksha and his army, when Dakshayani, had tried to stop his father Dakhsa from performing Dakshayagnam.
Ferocious Daksha ignored Dakshayani and continued performing the Yaga to insult and abuse Lord Shiva. Being intolerant by this, Goddess Parvati left the form of Dakshayani by entering into the sacred fire of Yaga, thus becoming ashes.
Lord Shiva then sent Veerabhadra to destroy each and every one coming on the way to demolish Daksha. Following Lord Shiva’s rules, Veerabhadra has finally cut down Daksha’s head. Nobody had a control over Veerabhadra and everyone was terrified by his anger and violence. Lord Vishnu and all the other Gods pleaded Lord Shiva to withdraw his extraordinary power, which is in the form of Veerabhadra.
As Veerabhadra has been created by Lord Shiva to destroy the Yagnya performed by Daksha, here Lord Shiva is portrayed as Dakshayagyaharamurti. Sometimes it is believed that Veerabhadra is himself Lord Shiva, because there is no other God which could replicate Lord Shiva’s anger. Thus according to the religious experts, the forms of Veerabhadra and Dakshayagyaharamurti belong to Lord Shiva.