The word "do" is sometimes used to mean to take part in a process or activity.
One might say "James wasn't very polite today" and someone might reply "James doesn't do polite". The usual phrase is "be polite". To say somebody doesn't "do polite" suggests he makes not the slightest effort to be polite. Politeness is an alien concept to him.
One may cook lunch or eat lunch, but sometimes people say "do lunch" meaning meet up and have lunch, or to take part in the lunching process.
If somebody says she doesn't "do Christmas" she will be understood as saying she does not participate in any of the observances common to the season. It is wider than saying one does not celebrate or observe Christmas.
In the song lyrics, the soldier could have said that he would make a sacrifice, the sacrifice of his life. To make a sacrifice, or offer or pay a sacrifice, are common ways of expressing the act of voluntarily giving up something. The word "do" is used instead.This, I think, is intended to mean that the soldier will take part in the whole concept. He will take part in the "worthy sacrifice". It prompts us to ask the question, in what way will he "do" the sacrifice? What part will he play?
He, the soldier is the victim. He is the sacrifice. His country has decided that his life is a price worth paying for the greater good. To have said "make a sacrifice" would imply it was of his own volition. Perhaps it partly was but perhaps rather than make a sacrifice he might have said be a sacrifice.
By using the phrase "do the worthy sacrifice" the lyricist is, I believe, inviting us to understand he was playing his part in the sacrificial process which the powers that be deemed worthy. His role was dual, both priest and victim. To have said "make a sacrifice" or "be a sacrifice" would give only half the picture.