This is a great question.

Child soldiering is a research area of mine. I have learned to be somewhat skeptical of claims about their use because sometimes even trustworthy academic researchers will repeat facts and figures that are actually false. I did some research this evening on the subject, but I must include a couple disclaimers beforehand: 1.) I am a specialist in Africa, not the Middle East; 2.) I don't have access to the entire range of research tools I'd use if I were to publish on the subject. I also apologize for the formatting of my post as the reddit editor limits my options:

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NEWSPAPERS

Several newspaper reports dating from around 1984 describe the practice. These are the first English-language sources that I have found on the subject. The most detailed comes from the NYT article below. I have excerpted some relevant bits:

Terence Smith, "Iran: Five Years of Fanaticism", The New York Times, February 12, 1984, Section 6; Page 21, Column 3:

HEIR TICKET TO PARADISE IS the blood-red headband and the small metal key that they wear into battle. ''Sar Allah,'' (''Warriors of God''), some of the headbands read in Farsi script, identifying the wearers as divinely designated martyrs who will use their keys to go directly to heaven if killed in the holy war against Iraq declared by their leader, the Ayatollah Ruhollah Khomei ni. The headbands and the keys are worn by young boys, aged 12 to 17, who are recruited by local clergy or simply rounded up in the villages of Iran, given an intensive indoctrination in the Shiite tradition of martyrdom, and then sent weaponless into battle against Iraqi armor. Often bound together in groups of 20 by ropes to prevent the fainthearted from deserting, they hurl themselves on barbed wire or march into Iraqi mine fields in the face of withering machine-gun fire to clear the way for Iranian tanks. Across the back of their khaki-colored shirts is stenciled the slogan: ''I have the special permission of the Imam to enter heaven.''

In dozens of interviews conducted by this reporter in recent weeks with Iranian exiles, academics and government and intelligence officials in the United States and Europe, the blind faith of these teen-age martyrs was frequently cited as symbolic of the fanaticism that is part of life today in the Islamic Republic of Iran. An East European journalist who witnessed one of these human-wave assaults, in which tens of thousands of young Iranians have gone willingly to their deaths, could hardly believe what he was seeing, as first one boy, and then another, detonated a mine and was hurled into the air by the explosion. ''We have so few tanks,'' an Iranian officer explained to the journalist, without apology.*

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David B. Ottaway, "Child POWs; Captured Young Iranians Languish in Iraqi Prison," The Washington Post, July 16, 1984, First Section, A1:

As Iraq braces for yet another expected Iranian offensive, Iraqi authorities today took a group of visitors, including Arab and western reporters, to a POW camp just outside Ramadi, 70 miles west of Baghdad. Among the more than 1,000 inmates were several hundred Iranians, 12 to 17 years old, who seem to have become the forgotten children of the war.

The Iraqi general in charge of the youth, who identified himself only as Gen. Amer, said Iran had shown no interest in having them returned and had denied there were any Iranian POWs at all.

Until his capture in March when Iraqi troops were taking back parts of the Majnoon islands in the marshlands of southeastern Iraq, Ahmed was a member of Iran's basij, an apprentice youth corps whose members reportedly have been used at times as human sacrifices to clear mine fields for the Revolutionary Guards who control the youths.

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Rezaei said he was one of those who was supposed to lead the charge across Iraqi mine fields but he was shot in the legs four times by Revolutionary Guard soldiers when he tried to flee the front line.

He said he had been given a dose of "martyr's syrup" before going to the front line. He said he did not know what it was but that it tasted like sugar and water, "the same as my mother gives me at home." He said he did not think there was any drug in it because this would be forbidden by Islam.

The willingness of children to charge across Iraqi mine fields to their likely death or serious injury has raised speculation in the Arab world and in the West that Iran is using drugs on them. None of the youth interviewed here today seemed to believe this was the case. But they did confirm many took the "martyr's syrup."

I've also found a number of references to articles written by the AP reporter Hanns Neuerbourg, however I don't have access to databases that draw from newspapers that syndicated his work. Hopefully another redditor can track them down? Here are some links to preview examples:

Hanns Neuerbourg, "Iran's child martyrs," Detroit Free Press, Monday, March 12, 1984, Page 5

Hanns Neuerbourg, "Child soldiers Young, fearless fighters become martyrs for Iran, who denies they exist," The Galveston Daily News, Thursday, March 15, 1984, Page 9

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ACADEMICS / NGOs / IGOs

Many academic studies that reference this subject either do not cite sources or do so inaccurately. This is extremely common and a source of great disappointment for people who are committed to careful documentation. For example, David M. Rosen recently published Child Soldiers in the Western Imagination: From Patriots to Victims (2015), one of a few that he has written about child soldiers. He writes:

During the Iran-Iraq War, Iran recruited some ninety-five thousand children above age twelve, and some as young as nine, to be used as human waves to clear areas of land mines.

He does not give a reference for this statement, however the following sentence includes a citation:

The official age of recruitment in Iran is nineteen, but government-allied paramilitary groups and even foreign Iranian allies such as Hezbollah systematically recruit volunteers with little concern about age.^2

That reference is a subsection of a 2001 report by the NGO Child Soldiers International (then known as the Coalition to Stop the Use of Child Soldiers) entitled "Child Soldiers Global Report 2001 - Iran", which was part of a larger document of which I am very familiar.

The article on Iran does not contain the figure of 95,000 children recruited during the Iran-Iraq War and it certainly does not suggest, as Rosen's summary implies, that their main purpose was to clean mine fields. Instead, CSI researchers write:

Boys as young as nine were reportedly used in human wave attacks and to serve as mine sweepers in the war with Iraq.

Their source, which I have seen repeated elsewhere, is: "The Abuse of Human Rights in Iran," London: House of Commons, Parliamentary Human Rights Groups, 1986, p. 41. Unfortunately, I do not have access to this document without making an inter-library loan request through a university library, but you might try yourself if you have the means.

A separate source that I have seen mentioned a few times is a subsection of a report by the IGO UNICEF entitled "Children as Soldiers" from the 1996 State of the World's Children report. UNICEF researchers write:

During the Iran-Iraq war, child soldiers, for example, were sent out ahead in waves over minefields.^18

Their source is a presentation given by the aforementioned AP reporter Thomas Hammarberg to the [Second] Regional Consultation on the Impact of Armed Conflict on Children in the Arab Region. You can find a summary statement of that consultation here, but it does not include comments from Hammarberg's presentation (nor would I expect it to) and it only abstractly refers to "Children used as instruments in armed conflict (i.e. spies, porters, mine detectors)." It is unlikely that a copy of Hammarberg's presentation is available, but again if you have access to a good university research librarian that person might be able to locate it.

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There are a number of academic studies on the Iran/Iraq war that mention this subject, but I am not qualified to comment on their accuracy or the reliability of their authors. I do not feel comfortable talking about them with any authority.

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TL;DR

Reports from Western newspapers around the time of the Iran/Iraq war and NGOs/IGOs seem to verify the claim that the Iranian military used child soldiers to clear minefields. However, I can't locate a primary source that would allow me to say definitively that it happened.