Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

Americans pronounce tragedy as TRA-juh-dee (/ˈtrædʒədi/). In "tragedy", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, and it's why Americans sound more relaxed than the textbook. So instead of TRA·juh·tee, you get TRA·juh·dee. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "He directed a modern adaptation of a Shakespearean tragedy".
Record yourself saying "tragedy" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "tragedy", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
In "tragedy", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. /t/ shifts toward /tʃ/ ("ch"), so TR sounds like "chr".
Stress falls on the first syllable, not the others. Stretch TRA — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.