Self answering... also a partial answer.
The process of taking Sannyasa is found in the book called the "Essence of Dharma Sindhu" hosted at the Kamakoti.org. But there is no mention of any scriptures from which the guidelines, Mantras etc are taken. Otherwise, the details is quite extensive.
Sanyaasa Grahana Vidhi:
Uttaraayana is stated to be the preferred time for initiating into
Sanyasa, especially for those who have Grihyaagni. Having located a
Sadguru who possesses Shanti and Danti o r Placidity and Self
Restraint, the aspirant Sanya si should learn Sanyasi Dharmas from the
tutelage and keep on practising Gayatri Japa, Rudra Japa and
Kushmanda Homa for three months and after attai ning Bahyaantara
Shuchi on one Rikta Tithi make th e Sankalpa: Amukasya Mama karishya
-maana Sanyaase neydhikaaraartham Chatuh krucchaatmakam praayaschi ttam Pratikruccham tatprachyamnaayaika Gonishkriya dwaaraaha
maacharishye Krucchaprtayaamnaaa Gonishk raya dravyam Viprebhyo
daatumahamtsrujey/
Thus hav ing given Go-Pratyaamnaaya,commence series of Shra addhas on
Ekadashi or Dwadashi at Brahma Ratri. As hramasastha has to perform
ChatuhKruccha followed by Ashta Shraddhas; Aapastambas and
Hiranyakeshiya s follow the Saankalpa Vidhi without Agnoukarana P
indaas and by Sankalpa Vidhi only. But Ashwalaayan aadis follow
Sapinda Paravana Prayoga; in this in Savya position they perform
Shraddhaanga Tarpana with Yava mishra jala in rivers and waterflows
sta ting: Brahmaanam Tarpayaami, Vishnum--; Maheshwara m--;
Devarsheen--; Brahmarsheen--;Kshatrarsheen--;
Vasoon--;Rudraan--;Adityaan--; Sanakam--;Sanandan am--;
Sanaatanam--;Pancha Maha Bhutaani--; Chakshu raadi
Karanaani--;Bhutagraamam--; Pitaram--; Pitaa maham--;Prapitaamaham--;
Aatmaanam-/
Having return ed home the Karta would then announce Desha Kaalaa di
and make the Sankalpa: Karishyamaana Sanyaaasaa ngatvey noushtaa
shraadhhani paarvana vidhinaannen aameynavaa karishye/
This would be like Naandi Shr aaddha and hence in Savya position
itself by using yavaas in place of Tilas. The opening Shraaddha is
meant for Satya Vasu Sanjnika Vishwa Devas involv ing two Naandi Mukha
Brahmanaas and naming (Vaana) of one of them to organise the Eight
Shraaddhas. In the Prathama Deva Shraaddha, the ‘Ucchaarana’ or
recital would be Brahma Vishnu Maheshwaraa Naan di Mukhaah
Sthaanekshanah priyataam/ The Second one is Rishi Shraaddha with the
Uccharana of Deve shi Brahmarshi Kshatrarshi yo naandi –mukhaah Stha
anekshana priyataam/ The third one is Divya Shradd ha addressed to
Vasu Rudraa- ditya Rupaa naandhi mukhaaya--/ The fourth one is
Manushya Shraddha to Sanaka Sanandana Sanaatanaadi----; the fifth one
is Bhuta Shraaddha to Prithivyaadi pancha Mahaa bh utaan –yekaadasha
chakshuraadi karanaadi chaturvid ha bhutagraamaa naandi mukha;the
sixth one is Pitr a Shraaddha to Pitru Pitaamaha Prapitaamahi naandi
mukha----; the Seventh Shraaddha is directed to M aatru Pitaamahi
Prapitaamahyo naandi mukha---; and finally the Eighth Shraaddha being
Atma Shraaddha and the Uccharana is: Atmaantaraatma Paramaatmaa nah
Naandi mukha----. After the Naandimukha, Padya is given to Vishwa De
vas with the Mantra : Sanyaasaartha maham Shraaddh am kurvey bruta
Dwijottamaah, Anugnaam praapya ush maakam siddhim praapyaami
shasvateem/
Then one Vishwa Deva Patra and Ashta Patras for are arranged for
Deva-Rishi-Divya-Manushya-Bhuta-Pitru-MaatruAtma to provide
Aasana-Gandhaadi Ahutis are offere d. This method is by way of
Sankalpa in the case of Apastambaas but Ashvaayanas perform with
‘Arghy apaatraa- sadana’. Pinda-daanaadikas also are not applicable to
Apastambaas. After the Ashta Shraddh a on the first day, the Sanyasa
Karmas on the foll owing day include kesha khandana , Nadi Snaana, ko
upeena dharana, danda dharana, kamandalu dharana, Achhadana Vastra
dhaaranaadi karmas. Then the Sanyasa Grahana Karya is followed by
the Maha Sankalpa : Asesha duhkha nivrutti niratishaya -ananda pra
apti rupa Parama Purushaartha praaptaye Parama Ham sa Sanyaasa
grahanam karishye/ Tadangatayaa Ganapa ti pujana punyaahvachana
Maatrukaa pujana Naandhi Shraaddhaani karishye/
The procedure is as follows : Recite the Mantra viz. Brahmaney namah,
Vishna vey namah, Rudraaya namah, Suryaaya, Somaaya, Atm aney,
Antaratmaney, Agnimeeley, Ishetvorjetwaa, Ag na Aayaahi Shannodevi
etc.; take three fistfuls of ‘Satthu Pishta’ or mix of cereals,
millets and pu lses, eat the Sattu thrice and touch the naabhi ;
recite again the Mantra: Atmaney swaha Antaraatma ney swaaha
Paramatmaney Prajaapataye swaaha; eat the mix of milk-curd-ghee-water
by the Mantras of t rivridasi once, pravridasi twice, divrudasi thrice
, then drink water saying Aapah punantu and finally state: Upavaasam
karishye/
Thereafter, in that order, are to be performed the following rituals:
Savitri Pravesha
The Karta would recite : Om Bhuh Savitrim pravishaami; Om Tat
Savaturvarenyam Om B huvah Savitrim pravishaami; Bhargodevasya dheemah
i; Om Swaha Savitrim pravishaami; Dhiyoyonah prach odayat Om
Bhurbhuvaswah Savitrim praveshayaami; Ta tsavatur varenyam Bhargo
Devasya dheemahi dhiyoyon ah prachodayat/
Viraja Homa
This is a highlight Homa in the conte xt of Sanyasa Grahana Vidhana
and is more or less the conclusive component of the Vidhana. Vira ja
Mantra : It is with this Mantra that forty clim actic Ahutis to
Agnideva are executed with a wide variety of Dravyas
Sarva Tyaga Vidhi:
Total Renunciation starts with the recital of the Maasa-Tithi-kaalas
by the Karta as he would leave three handfuls of water in a
Jalaashaya : Aparoksha Brahmaavaaptaye Sanyaasam Karomi/--Yeshahavaa
Agnissurayah praanam gacchasw aa, Om swaamyonimgaccha swaahaa/
Viraja Homa
and finally, the Praisocchara:
Praishocchaara: The terminal acts of Sanyasa Vidha ana of
Praishocchaara of the new Sanyasi are as f ollows: First with leaving
water in the Flow with the Mantras thrice in three tones of low-medium
an d loud voice: Om Bhuh Samnyastam mayaa, Om Bhuvah Samnyastam
mayaa, Om Swaha Samnyastam mayaa, Om B hurbhuvaswah Samnyastam mayaa/
Then the Shikha is unfurled and cut; the Yagnopaveeta is taken out b y
the raise of his hands above the shoulders and k ept in his hands
reciting the Mantra:
For all these above processes, i have omitted a huge amount of actual details, because otherwise, it makes the answer exceptionally long.
Those who want to read in details can read this chapter of the book "Essence of Dharma Sindhu"
But, i am interested to know from which scriptures all these Mantras and procedures are taken. So, that part of the question is yet to be answered.