The definition of a serial killer:
A serial killer is defined as a person who murders three or more people over a period of more than 30 days, with a "cooling off" period between each murder, and whose motivation for killing is largely based on psychological gratification.
(
https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Serial_killer.html)
Based on official definitions, and with 1 human being murdered, Arias is not a serial killer. The type and ferocity of the murder itself is not a consideration at all. It comes down to the numbers killed. 3 or more over 30 days meets the criteria.
Susan Wright murdered her husband with nearly 200 stabs of 2 knives and then tried to hide the murder by burying him, though only partly, right in the dirt outside the patio. She's not considered a serial killer either.
Melanie McGuire murdered her husband then chopped him up into pieces and put his body into 3 suitcases and dumped them into a body of water. She too is not a serial killer, though she certainly used more than 29 cuts to get a man's body into small enough pieces.
Sabrina Zunich was 17 yrs old, was having an affair with her foster father, then stabbed the foster mother to death 178 times
, and in front of the couple's 13 yr old biological daughter. She's not a serial killer either. She just got 30 yrs to Life, as did the Husband who initiated the affair and encouraged the murder.