The 35-year-old hip hop star reacted badly after being filmed by the two fans on the driveway of his New Jersey property.
In two videos, which have since gone viral online, Joe was seen driving after the pair, who had attempted to make a quick getaway in their own vehicle. The rapper then got out of his car and chased after them on foot.
After catching up with their car, a furious Joe, who was carrying rocks in his hands, told the terrified fans, "This is not the internet. I will kill one of you."
One of the fans was then heard apologising to the rapper and telling him, "I understand."
The Pump It Up musician also hit the headlines last week (end24Jul16) after releasing another diss track in which he mocks Canadian rap superstar Drake.
Writing on Twitter after the incident, one of the fans who visited him at his home explained what may have caused some of Joe's anger.
"He got so heated when I threw drake lyrics at him. He really high speed chased us," the fan, with the Twitter username @RedaKidProdigy, posted.
After the video appeared online, it was shared by social media users so extensively that Joe's name swiftly became a top trending topic on Twitter, while others used photo editing software to alter stills from the video to create internet memes featuring the rapper.