Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce cutting as KUH-tuhng (/ˈkʌɾɪŋ/). In "cutting", 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 one of the defining features of casual American English. It comes out as KUH·tuhng. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "I measured the window twice before cutting the new curtain rod".
Record yourself saying "cutting" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Quickly bounce the front of your tongue against the roof of your mouth. Don't stop the airflow — just a quick tap.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "cutting", 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.
Stress falls on the first syllable, not the others. Stretch KUH — 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.