In which avastha/bhaava does Chinnamasta falls? Does it belong to
No, she belongs to the Dakshina-amnaya, as pointed out by Partha. Whereas Tripura Sundari is an Urdha-amnaya Goddess.
VAravAnaliya Tantram gives the following Amanya-Bheda:
DakshinAkAli, BagalAmukhi, ChinnamastA, TArA, MAtangi and BhadrA are
deities of Dakshina-Amnaya (Southern amnaya). Shodashi and Bhairavi
are Urdha-Amanya (higher amnaya) Goddesses whereas Bhuvaneswari,
AnnapurnA etc are Purva-Amnaya (eastern amnaya) Devis.
So, ChinnamastA has separate worship.
ChinnamastA or ChinnamastikA (also known as Prachanda ChandikA) is a Supreme Goddess
She is the 6th MahAvidyA.
The Shakti Samgama Tantram 4.51 states about her the following:
yatha chinnA tathA kAli tathaiva sundari parA |
samdishtA chaturthanAm nahi bhinnatA ||
Who is ChinnA she is KAli
and she is the supreme Tripura Sundari and she is again TArA -- Among
these four, there is no difference.
So, to compare such a Goddess to Yakshini is not at all right.
In Bhairava Tantra's "Chinnamasta Trailokya Mohana Kavacha", we find that the Trinities worship the Goddess.
We have the verses:
Trailokyavijayam nAma kavacham sarvamohanam |
sAkshAt surAsurajayapradam ||
trailokyavijayi vibhuh |
BrahmA nArAyano rudro dhArnAt pathanad
This armour named "Trailokyamohana' is capable of enchanting all. It
is endowed with all-knowledge and gives victories over Devas and
Asuras. The one who reads it or wears it becomes the winner of the
three-worlds. Lord Brahma, NArAyana and Rudro all wear and read it.
Goddess ChinnamAsta's worship and Mantra
The most celebrated mantra (or VidyA) for the Goddess is a 16-letter mantra. This mantra is mentioned in YAmala Tantrams as well as in Viswa SAra Tantram.
The greatness of this VidyA is as follows:
prachandachandikAm vakshye sarva kAma-phalapradAm |
prasAda mAtrena shiva eva bhaven narah ||
aputro labhate putram
Kavitvam cha supAndityam labhate nAtra
By simply getting the grace of the all-desire-fulfilling Prachanda
ChadikA (or ChinnamastA) a man becomes Shiva. The childless gets
child; the poor gets wealth and expertise in poetry and scholarly acts
are obtained without doubt.
PurashcharjArnava, Taranga 9
The mantra itself (in codes) and it's various applications are found in the following verses:
Lakshmi lajjAm tato mAyAm mAtrAdvAdasikAmatha |
cha mAye phat swAhayA yute || (mantra code ends here)
Lakshmi bijam yadA AdyAm syAt tadA
shrih sarvatomukhi ||
LajjA bijena chAdyena vasyatAm yAnti
MAyAbijena chAdyena mahApAtakanAshanam |
MAtrAdvAdashikAbijamAdyAm syAnmuktidAyakam ||
If Shrim is at the start [of the mantra], [the mantra] gives all-round
prosperity; if Klim is at the start, it gives the power of attracting
all women; If Hrim is at the start, then it destroys all mortal sins;
and if Aim is at the start, the mantra is giver of liberation.
And, if Om is at the start of the mantra then that is a giver of Bhukti-Mukti both.
TArAdyA shodashi chyAnyA bhavet sapta dashAkshari |
mahAvidyA bhuktimukti kari sadA ||
If OM is added at the start of the 16-letter VidyA of ChinnamstA, then
that mantra becomes giver of worldly pleasures and liberation both.
ViswasAra Tantram verse quoted in the same text
There are other mantras for the Goddess given in MahAkAla SamhitA etc.
ChinnamastA - the most fierce deity
ChinnamastA is by far the most terrible deity. So, no weak hearted person may embark upon her worship. It can be fatal, if things are done without proper knowledge, and without a competent Guru's guidance.
For this point it's stated:
NAtah paratarA kAchidugrA devi bhavishyati |
TasmAd asaktairmanur janai grAhyeyam kathanchana ||
vA dvayorekataram bhavet |
There is no deity which is more fierce than ChinnamastA. That is why the faint-hearted must never accept her mantra and worship her. In
her SAdhanA, either Siddhi or death is inevitable.
Further, we also have the following warning regarding the ferocity of the Goddess:
PrachandachandikAmeva dhyAtvA yastu na pujayet |
shirashchitvA devi pivati shonitam ||
Without DhyAnam other deities can still be be worshipped. But, who
does not worship Goddess Chinnamsta duly with her DhyAnam, will get
his head chopped off.
So, better stay away from her worship unless you have the guidance of a highly competent Guru.