In the MT for Psalm 118:27,
אל יהוה ויאר לנו אסרו-חג בעבתים עד-קרנות המזבח
the preposition translated in the KJV as "even unto" is עד, which means "up to" or "until" in current American usage. If the intent had been to say that the dedicated animal was tied to the corner of the altar, the preposition would probably have been על, or possibly ל, as in Deuteronomy 6:8:
וקשרתם לאות על ידך והיו לטטפת בין עיניך
"and you shall tie them for a sign on your hands and they will be an ornament between your eyes", or as in Numbers 15:38 (NIV) where על is also used:
Speak to the Israelites and say to them: 'Throughout the generations to come you are to make tassels on the corners of your garments, with a blue cord on each tassel
I would suggest that a careful reading of the KJV's "even unto" in fact does not imply that the animal was tied to the corner of the alter.
Not withstanding, one commentator, R. Moses Isaac Tedeschi, in his book "Moses Began", M. T. Seitz, Trieste, 1870, suggested that the animal was tied to the corner of the altar. However, Amos Hacham, in the "Daat Mikra" refutes this, saying that there is no support for this view in either the MT or the Talmudic tradition.
Regarding the KJV translation, it sounds belabored to the modern Hebrew speaker. In any event, we need to read the verse in the context of the whole psalm and in particular, the context of verse 26.
The whole psalm is almost certainly a pilgrim psalm, sang by family or village groups making one of the three annual holiday pilgrimages to Jerusalem. The word translated as "sacrifice" in the KJV is in fact חג, meaning literally "holiday", not "sacrifice". However, over the course of time, the word חג, "holiday" became synonymous with the major event of the day, the holiday sacrifice, as in Exodus 23:18 (KJV) where חג is also used:
Thou shalt not offer the blood of my sacrifice with leavened bread; neither shall the fat of my sacrifice remain until the morning.
which the NIV renders as:
Do not offer the blood of a sacrifice to me along with anything containing yeast. "The fat of my festival offerings must not be kept until morning
The first 24 verses of psalm 118 are a prelude to the ultimate five verses. Verses 25 through 27, and probably to the final verse, 29, are responsorial. Verse 25 is an exclamatory supplication made by the pilgrims at the end of their journey to Jerusalem, just before they enter the temple with their holiday offering.
LORD, save us! LORD, grant us success! (NIV)
Verse 26 is the spoken by the priests who greet the pilgrims into the temple:
Blessed is he who comes in the name of the LORD. From the house of the LORD we bless you. (NIV)
In response to verse 26 spoken by the priests, verse 27 is spoken by the pilgrim group. It is both a confession of faith that only the LORD is god and it is He who has saved the group, allowing them to reach the temple, and an exhortation to the members of the group to proceed to the altar with the bound festival sacrifice.
The LORD is God, and he has made his light shine on us. With boughs in hand, join in the festal procession up to the horns of the altar.
Note that the NIV, and a few other modern translations, translate בעבתים as "with boughs", referring to the bound palm fronds (the lulav) that were used on holidays, and particularly on Tabernacles, rather than to the bound sacrificial animal. This translation possibility appeals to me because it resolves the redundancy of the "bound sacrifice" (אסרו-חג) that is "bound" up to the altar, into two symbols of the holiday that were bound, the lulav and the sacrifice.
So, the answer to your question, is that this is a pilgrimage festival sacrifice that was eaten by the pilgrims themselves, after the priestly portions had been taken, most likely a bull or ox, brought most likely on Tabernacles, but possibly also on Passover or Weeks.