There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
askat-
verb. to rend, break asunder
sakkat-
verb. to rend, break asunder
narka-
verb. to rend
A verb in The Etymologies of the 1930s glossed “to rend” derived from the root ᴹ√NARAK “tear, rend (tr. and intr.)” (Ety/NÁRAK; EtyAC/NÁRAK). In The Etymologies as published in The Lost Road Christopher Tolkien gave the form as narki (LR/375), but Carl Hostetter and Patrick Wynne corrected this to narka in their Addenda and Corrigenda to the Etymologies (VT45/37).
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
The verb ᴹQ. terhat- “break apart” appeared in The Etymologies of the 1930s, a combination of ᴹQ. ter “through” with the root ᴹ√SKAT “break asunder” (Ety/SKAT). Its past form terhante “broke” appeared in earlier versions of the Lament of Atalante from the 1930s (LR/47, 56). In versions of the poem associated with The Notion Club Papers from the 1940s, Tolkien revised terhante to askante “sunder-broke” (SD/310), and in the final version of the poem he had sakkante “rent” (SD/246). The past form sakkante is difficult to puzzle out, but askante is probably based on an augmented form askat- of the root ᴹ√SKAT.
Neo-Quenya: For purposes of Neo-Quenya, I would retain both terhat- “to break apart” and askat- “to rend, break asunder” as near synonyms, both more distinctive than the basic verb ᴹQ. hat- “break asunder”.