I think the horse in the Ashwamedha was killed with knives. The Somavajapeya involves suffocating the sacrificial animal if I am not mistaken.
Do scriptures specify how animals should be killed during the sacrifice?
Yes, the horse in the Ashwamedha is suffocated with a cloth.
Taittiriya Brahmana 3.9.20:
tArpyeNAshvam samjnapayanti | yajno vai tArpyam | yajnenaivainam samardhayanti | yAmena samnA prastotA'nUpatiSThate | yamalokam evainam gamayati
They (the Samitars, the slaughterers) kill the horse (literally: cause the horse to acquiesce) by means of the tArpya cloth. The tArpya cloth surely is the sacrifice. They thus abundantly provide him with (the essence of) the sacrifice. The Prastotar worships (the horse) by singing the Saman that belongs to Yama. He thus sends him to Yama loka.
As you can see, they really kill a real horse and it's not some metaphorical description. The reference to Yama loka proves this. The soul of the horse goes to the world (loka) of Yama, who is the god of death. There is no reason to interpret these words metaphorically.
The Kings does Ashwamedha Yagya and after that they release that Horse, and till where the Horse goes that land is claimed by the King if anyone opposed he has to fight with the Army of the King who did Ashwamedha Yagya.
the translation of the word 'medha' is often not interpreted as sacrifice. There are words like 'purushamedha' and 'sarvamedha'. Sarvamedha definitely doesn't mean sacrificing everyone.
Please see the second answer of this question, which is very correct and it related directly to Dharm.
You can take a look at this link on Google Books.
There is no animal sacrifice in Vedas. Some indologists have put the law of sacrificing animals in Vedas by wrong translations. In reality, animal sacrifice in yajnas is prohibited.
First of all, the synonym of Yajna used in Vedas is ‘Adhvara’ which means ‘non-killing”. Nirukta 1.8 says ‘dhvar’ means kill, and ‘Adhvara’ denotes the negation of killing (which is non killing).
I find plenty of Vedic verses which calls ‘Yajna’ as ‘Adhvar’ (means Non-killing), example of such verses are: Atharva Veda 1.4.1, Atharva Veda 3.16.6, Atharva Veda 5.27.8, Rigveda 3.10.7, Rigveda 3.16.6, Rigveda 4.6.1, Rigveda 5.49.4, Rigveda 1.74.4 Yajurveda 1.24, Yajurveda 3.11 etc.
Mahabharat, Shantiparv 265.9 “Liquors, fish, mead, meat, rice cooked with sesamum seeds- all these have been inserted into Yajna by the wicked people. Vedas have not prescribed their use in Yajnas”.
Lord Krishna in Srimad Bhagvatam 11.21.30 says, “People who find enjoyment in violence, out of wickedness and for gratification of their pleasure they slaughter animals, offer the meat in Yajan’s….”
So animal slaughter is completely prohibited.