Sumbhak was slain (by Rama) because he was making penance which was forbidden to him by Vedas as he was a "Shudra". (Uttara Kandam, Chapter 76).

Looking at his hand Rama said the Sanskrit slogan "Oh right hand, you kill this Asche Shudra unhesitatingly as killing this Shudra is the only way to get back the life of the deceased Brahmin boy. Are you not one of the limbs of Rama?" (Valmiki Ramayanam)

Complete Story

After killing the demons king Ravan, Ram returned to Ayodhya. many sages had arrived there to bless him on the occasion of his crowning ceremony. sage Vashishth was one of them. as Ram was conversing with the sages a brahmin arrived there with the corpse of his son and wailed---"o son! your death is certainly due to some flaw of Ram. now, your mother and I have decided to give up our lives as there is no point in living." Ram's heart was filled with grief and he asked sage Vasistha as to how the brahmin could be helped. sage Vashishth revealed to Ram that the brahmin's son had died a premature death because of Shumbhak. Vashishth said--"Shumbhak is a shudra by birth, but he is doing an austere penance. shudras are not entitled to do penance in all the three yugas, except the kal-yug. so, only his death can bring back the brahmin's son alive." Ram instructed both his younger brothers--Laxman and Bharat, to look after the state's affairs in his absence and went in search of Shumbhak boarded on his pushpak vimaan. Ram saw a man doing penance at the shore of a reservoir. he landed his pushpak vimaan and went near that man. he introduced himself and enquired about the man's identity--Ram asked--why are you doing such an austere penance. who are you? without moving the man replied that he was a shudra named Shumbhak. he said---- I am desirous of attaining to devaloka and hence I am doing this penance. Ram took out his sword and severed Shumbhak's head. all the deities hailed Ram and the brahmin's child became alive once again.

Note: This Rama, who mercilessly took away the life of Sumbhak for no other fault than that of making penance is held as the Avatar (incarnation) of Vishnu! If there were kings like Rama alive now alas! What would be the plight of those who are called "Shudras?" But then we have Big Brahmins like Nehru and Vajpayee to take the place of Rama !

After some new input of information, I find that tradition does treat uttar kand as a part of ramayan. The reason is Gowswami Thulasidas the author of RAMAYAN in HINDI does writes the uttar kaand. THIS MEANS, THAT TRADITIONALLY UTTAR KAND MUST BE A PART OF RAMAYAN... MY QUESTION : If Shree RAM CHOPPED OFF Shumbhaka's head because he chanted vedas being a SHUDRA Why did Shree Ram did not chop off the head of Rishi Jabali who was not a brahmin but still studied the sacred vedas. ANOTHER Question : Why did Shree Raam not chop of the head of Rishi Agasthya who was a DHOBHI or Shudra by caste. Another Question : If Shree Ram believes the Sudhra is inferior, then WHY DID HE BANISH Maa SITA for the sake of a dhobi who is a shudra. SO, THERE IS SOMETHING DEEPLY EMBEDDED IN SAYING THAT LORD SHREE RAM CHOPPED OF THE HEAD OF SHUMBHAKA just because he is a sudhra. One needs to find that out