ἱερουργοῦντα is, as you probably well know, a participle of ἱερουργέω - which in turn is the verb form of ἱερεύς, meaning priest. Thus ἱερουργέω means something like "to act as a priest" (or "to priest"). The participial form is translated as "ministering" in the King James Version, "in the priestly service" in the RSV. The Orthodox New Testament, a fairly literal version compiled by Greek Orthodox nuns, translates the full passage:
But I am writing more boldly to you, brethren, in part, as reminding you, because of the grace which was given to me by God, in order for
me to be a liturgist [λειτουργον] of Jesus Christ to the nations,
ministering as priest in sacred sacrifice [ιερουργουντα] the Gospel
of God, that the offering of the nations might be acceptable,
sanctified in the Holy Spirit. (Romans 15:15-16)
According to the concordances I have access to, neither the verb nor any of its forms (participial included) appear anywhere else in the New Testament or anywhere in the Septuagint.
The late Eastern Orthodox hierarch Archbishop Dmitri Royster dedicated a couple of sentences to this occurrence of ιερουργουντα in his commentary on Romans (St. Paul's Epistle to the Romans: A Pastoral Commentary). He suggests a translation of "sacrifice" (p. 374):
The next word translated "minister" is hierourgounta, participle of
hierourgeō, "sacrifice" or "offer in sacrifice", related to hiereus, "priest", as in Hebrews 7, and to hierateia, "priesthood", in Hebrews 7:5 and a number of places in the Old
Testament (Exodus 29:9; Ezra 2:62; Hosea 3:4, and elsewhere). The
object of this verb si "the Gospel of God," thus, "serving as a priest
of the Gospel." Now, since a priest offers sacrifice (prosphora),
his, as he goes on to say, is the sacrifice of the Gentiles, offered
up as the work of his ministry ...