Since you really don't say which verb in Heb.1:3, but you do leave a clue it is in the aorist tense, I am going to go with ποιησάμενος or poiasamenos, which is a aorist middle participle. It comes from the word "to make". The use of the middle suggests that Christ Himself in His own person made the purification. The aorist points to the completed action. Aorist expresses the action which occurred before the main verb, ἐκάθισεν or ekathisen, meaning "to sit down, to take one's seat."
"He is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power. After making purification for sins, he sat down at the right hand of the Majesty on high," Hebrews 1:3
"ὃς ὢν ἀπαύγασμα τῆς δόξης καὶ χαρακτὴρ τῆς ὑποστάσεως αὐτοῦ, φέρων τε τὰ πάντα τῷ ῥήματι τῆς δυνάμεως, δι᾽ αὑτοῦ καθαρισμὸν τῶν ἁμαρτιῶν ποιησάμενος ἐκάθισεν ἐν δεξιᾷ τῆς μεγαλωσύνης ἐν ὑψηλοῖς," Hebrews 1:3 Greek.
Once again, someone is spouting Greek who does not have the faintest clue how to read or translate the Greek. Translation is not about looking up individual words in the Blue Letter Bible or Strong's, or even worse, quoting some preacher who is twisting the Greek to prove his own doctrines.
Christ is NOT making purification without ceasing. You are thinking of the imperfect tense. Imperfect is an ongoing action in the past. Although there are some other uses of the aorist in Greek, the MAIN use, including Heb 1:3 is a completed action in the past. And the present tense can also infer an on-going action in the present.
I do wish people would learn Greek, esp. the syntax and grammar, including verbs, noun cases, and every Greek student's favourite (NOT!) participles! Then we could have some decent discussions, instead of people passing off a knowledge of Greek, which is in fact totally wrong!
However, after looking at the Greek for Hebrews 7:24-25, I do agree that it is the continuing or unending state. In other words, the action of purfication was a ONCE for all time action. But Christ being the high priest is forever, a continuing state. He intercedes, but the sacrifice for sin was done on the cross, forever! Christ intercedes, but he longer has to make a continuing sacrifice. That is RCC doctrine, and the Greek proves it totally wrong.