Direct Answer
The traditional story says Origen made himself a eunuch when he was young, and the article on Origen's life and reputation notes that Eusebius assumed the story was true. But the same article also says the story stands in sharp tension with Origen's own words, where he condemns Christians who take Matthew 19:12 literally and mutilate themselves.
Why the Question Is Complicated
This is not a simple yes-or-no question if we are staying with that source discussion. The article says the story was spread by Bishop Demetrius after his controversy with Origen. On its own, that would make the report suspect. But the article also says it cannot be dismissed lightly because Eusebius assumed it was true.
So the evidence is mixed: an early church historian reports or accepts the story, but Origen's own surviving teaching sounds like the opposite of what the story claims.
What Eusebius Said
The article summarizes Eusebius as saying Origen did this in youthful zeal, taking Jesus' words about eunuchs for the kingdom of heaven literally. The alleged motive was that Origen wanted to teach both men and women without fear of temptation.
What Origen Himself Said
The strongest counterweight is Origen's own Commentary on Matthew. The article quotes Origen criticizing those who literally make themselves physical eunuchs. He says such people act without understanding, bring reproach on themselves, and show an excessive love of discipline. The article then comments that it is difficult to believe the man who wrote those words had done the very thing he condemns.
Careful Conclusion
A careful answer should say this: the old story exists, and Eusebius accepted it, but the claim is treated as doubtful because it conflicts with Origen's own explicit teaching. It is better to call the claim disputed than to state flatly that Origen was a eunuch.
Read the Evidence Yourself
The main source for this answer is the Origen article linked above. Readers should compare the short answer with the source excerpt and the full linked article before treating the question as settled, especially where later summaries of Origen disagree. For broader historical context on major early Christian figures, see Who's Who in the Early Church?.