I noticed in other parts of India, many Brahmins take pride in Parashurama and worship him a lot. However, we don't appear to do the same. We don't disrespect him, but we don't give him the same level of importance. Why is that? I think as Iyer Brahmins we need more of that warrior spirit Parashurama has.
Ucchista,Rudramalaya,Haramekhala tantra states that Parashurama is a direct avatar of Ganapati hence He removes all obstacles.
Renuka Devi the mother of Parashurama is considered an incarnation of Devi Chinmasta and Jamadagni the father of Parashurama is considered an incarnation of Kalagnirudra.
Actually some part of this does explain the beheading of Renuka Devi..if she is an incarnation of Devi Chinmasta, the beheading makes perfect sense as Devi Chinmasta doesnt have a head.
Seems like may be Her incarnation on earth was over and Jamadagni ordered Her beheading to reinstate Her to Her original form of Devi Chinmasta.
Regarding to warrior spirit..that depends on a person's guna.
I dont think its about just praying to an Avatar and to imbibe His actions.
Parashurama was 50% Brahmin and 50% Kshatriya due to being of Mixed Varna ..father Brahmin, Mother Kshatriya..also Renuka Devi ate the payasam which was meant for Her mother..Her mother switched the payasam..so Renuka Devi ended up eating a payasam that was supposed to bring forth a powerful Kshatriya..hence Parashurama was born.
And Renuka Devi's mother ate the payasam that was meant to bring about a brahmana with sattva qualities hence Vishwamitra waa born.
So you can see the Brahmana portion in Parashurama genetically was 50% but the guna portion for a Kshatriya was much higher.
Anyway Tantra text link Him with Ganapati..so all the more He is swift in removing obstacles.