We used “underdog” as a noun, not a verb (“Do an underdog!”, that kind of thing).
I’m in my mid thirties and grew up in Toronto.
I was a kid in the 1950s in central Indiana. I never heard of it. Our dangerous swing thing was attempting to leap out of the seat at the top of the forward motion. It seldom ended well. We had all the dangerous devices; the merry-go-round, the teeter-totters, and the hard metal swing seats. None of them had soft beds of wood chips. It was just hard ground underneath.
I heard about kids getting hurt on the merry-go-round and the teeter-totters, but I never met anybody it happened to.
I once tried to turn around at the top of the slide, to slide on my belly. Somehow, I fell off, and I landed flat on my back.
california native 60’s-70’s swingset age. Don’t recall doing it, never heard the term used as such before
South central Wisconsin, late 60’s, never heard of it, but then I didn’t do too much swinging growing up.
In Vancouver in the 1970s, we called it “underducking.”
Minnesota - 70’s
Yep, Underdog, verb only
Yes, giving a friend a buck on your bike. “Want a buck?”
Same here- Western NY, late 80s and early 90s. I remember learning the term from my cousin when I was maybe 5 or 6. It was used in reference to a tire swing. My cousin lived in a different town. I don’t remember if kids at my school used “underdog” or not.
Mid-90s in CA. We did this all the time, and like a couple others, it was appropriate to yell “Underdog!” as you ran under the swing.
Born in 73, childhood in suburbs of St. Louis. I’ve never heard of the term or witnessed the action.
Pittsburgh, early 90s, called it an “underduck”, noun only.
For those that aren’t clear on it, the purpose isn’t to get kicked in the face. It’s to push the swinger as high as possible. The ancillary goal, as it is with so many things in life, is to *not *get kicked in the face.
Uhh never heard of this and thought it was going to be a thread on some obscure sexual term 
Damn.
80s kid in coastal NC.
70’s kid who grew up in Wisconsin. Never heard the term “underdogging.”
I liked swinging, but never trusted my brother or sister to push me. They’d go too far and I figured I’d end up swinging all the way around and kill myself. I was pretty sure my older brother and sister secretly wanted me dead.
I grew up in the 80s and 90s, I s’pose, in Central-ish Ohio. My cousins, brothers, and I would always “underdog” each other. I don’t think we ever used it in the gerund form, it was either “Underdog me,” “Playing Underdog,” “Giving him an Underdog,” etc.
IIRC, they were great fun. We had an accident only once, when kicked my cousin in the face when he didn’t run under fast enough (for whatever reason). Laughter all around. 
Southern Ontario, 1960s. We didn’t call running under the swing underdogging, but I recall a TV cartoon beaming across from Buffalo that starred a superhero dog named Underdog who popped pills as a pick me up.
No kiddin’. That was a thrilling moment, when the chain did that little ‘clink’ as the links kind of folded up together. I think I left my stomach up there several times!
At our school, we would do that but also hold one side of the chain briefly before jumping to the ground, for some reason.
Southeast WI, 90s.
The verb was to “do an underdog” or rarely to “give an underdog”.
In my first neighborhood there was the special thrill of synchronizing swings with your partner until both of you could get the entire swing to rock back and forth, legs lifting from the ground. (It was a trailer park, and none of us had a swing set that was cemented down or well-buried. Terrifying in the best way, and I don’t remember any casualties.)
I grew up in New England during the 80s/90s.
Never heard of the term, nor anyone doing this. How old are the kids doing this? Kids usually don’t need to be pushed on swings any more by first grade and this sounds like the sort of thing kids older than that would think to do 
Southwestern VA, born 1963. Never heard of it.
I grew up in Michigan in the 80s and 90s and was quite familiar with the term. Though I ought to add that I learned the term from my father who grew up in Ohio, central Ohio I think.
I live in NE Ohio, grew up in the early 90’s and never heard of the term.