Below is at least one source version which is the origin of the song having been written by Nathan Terrey (or Torrey) which also references Mirick. It is presented with a fuller narrative than quoted below, but I've omitted some more irrelevant portions. It is quoted from the July 11th, 1886 edition of The Chicago Tribune (link):

FAMOUS YANKEE POEMS.

Springfield (Mass.) Republican: A correspondent asks us to reproduce the poem of "Springfield Mountain," to which David A. Wells alluded in his speech at the anniversary banquet. We can do no better, therefore, than to quote Mr. Wells as follows: And then, if it is the more comic, as well as the poetic side of human nature that is to be sought, what can be more organically ludicrous than the famous poem or elegy of "Springfield Mountain," which has almost become a classic in English literature; and without a sufficiently proper notice of which, any historical review of Springfield would, it seems to me, be manifestly most incomplete. This elegy was written by one Nathan Terrey, a citizen at the time of Springfield, about the year 1761, in commemoration of a tragic occurrence that caused a great local sensation at the time--namely: the death from the bite or a rattlesnake of the son of Lieut. Mirick, who resided in that part of the town which was then known as "Springfield Mountain," and which was afterwards incorporated as a town by itself under the name of "Wilbraham" .... There have been many versions of this doggerel, but the following, which with your permission I will read, is believed to be the most authentic:

"SPRINGFIELD MOUNTAIN."

On Springfield mountin' ther' did dwell
A likely youth, was known full well.
This youth, his age was twenti-one,
Was Leftenant Mirick's onley son.

On Friday mornin' he did go
In to the meadow for to mow,
And as he turned around, did feal
A pisin sarpent bite his heal.

This youth he soon give up the ghost,
And up to Abraham's bosom did post--
A cryin' all the ways he went--
"O crewel, O crewel! O crewel sarpent!"

So soon his careful father went
To seat his son with discontent,
And there his onley son he faound
Ded as a stun a pon the graound.

His father vieude his track with great consarn
Where he had ran acrost the corn;
Uneven tracks, where he did go,
Did appear to stagger to and frow.

The seventh of August, sixty-one,
This fatal axsident was done.
Let this a warning be to all
To be prepared when God does call.

When he received his dedly wond
He dropt his sithe a pon the ground,
Tho all around his voys ware hered
None of his friends to him apered.