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Here it is ... footage showing Conor McGregor stomping out a cell phone in front of the Fontainebleau hotel in Miami -- and it's LOUD.

You don't only SEE Conor putting his foot down on the phone, you HEAR it -- two thunderous booms as McGregor slams his designer shoe down on the phone around 5 AM Monday morning.

You can also see and hear the alleged victim, Ahmed Abdirzak, plead with McGregor -- "Let me get my phone, man!"

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Abdirzak tells TMZ Sports he was just trying to snap a pic of Conor on his cell phone when the UFC star lured him in by appearing to offer a handshake, but instead snatched the phone and smashed it.

As we previously reported, cops were called and eventually located McGregor at a nearby mansion where he was staying with his family.

McGregor was arrested for robbery/strong-arm and criminal mischief over $1,000 (2 felonies) ... but his attorney downplayed the incident, calling it a "minor altercation."

If convicted on both counts, Conor is facing up to 15 years in prison for the robbery/strong-arm charge ... but he doesn't seem too concerned.

In fact, he went out for a jog after he was released from jail.

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It's not Conor's first brush with the law -- he was arrested in 2018 for throwing a steel dolly at a UFC bus in Brooklyn.