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You can hear this story/claim stated in various way, from just regular troops doing it, to just penal battalions, to strenuous denial nobody ever did this in the Soviet army. (Just look at a Quora thread.)

So what sources do we have (besides that story Zhukov supposedly told Eisenhower) on this issue?

I suspect sources covering Soviet penal battalions are closest to being relevant, because Wikipedia's article on the latter says

the penal battalions usually advanced in a frenzy, running forwards until they were killed by enemy minefields, artillery, or heavy machine-gun fire.

It does cite a book for this (Suvorov, Viktor, Inside The Soviet Army, Hamish Hamilton (1982), ISBN 0-241-10889-6), but not a precise page therein. Given the general scope of the book, I'm not convinced it has more details on this issue.

There are a few recorded instances of Soviet penal troops being intentionally sent over mines, at least according to survivors:

It is hard to judge
whether there was a deliberate sacrifice of penal soldiers, but Pyl’tsyn describes how
Batov, commander of the army to which his penal battalion was attached,
deliberately sent its soldiers—all of them temporarily demoted officers—across a
minefield, where they suffered 80% casualties. Pyl’tsyn, who also advanced across the
minefield but survived without a scratch, regarded this order as criminal and claims
that tanks with ploughs for making passages in the minefield were actually available.
The survivors of this action were not pardoned because Batov would not release an
uninjured soldier from a penal unit. Significantly, Pyl’tsyn does not reproach his
superiors for a mission in which the penal company he commanded spearheaded the
attack across the Oder River. Only four men survived without injury by the time they
had captured the bridgehead, while Pyl’tsyn himself was gravely wounded in the head.

Quoted from: Alex Statiev, "Penal Units in the Red Army", Europe-Asia Studies, 62:5,
721-747

The full name of the soldier is Aleksandr Pyl’tsyn, and the story is cited to his memoirs in Russian:

• Pyl’tsyn, A. (2003) Shtrafnoi udar ili kak ofitserskii shtrafbat doshel do Berlina (St Petersburg, Znanie).

"Batov" refers to the commander of the 65th Army, Pavel Batov.

I'm not sure if there are other stories corroborating something like this.