根こそぎ literally means “with the roots,” describing something being torn out entirely from the ground. In the song, the typhoon blows down even old trees and carries them away 根こそぎ, making the storm feel brutally powerful and unstoppable.
It is a vivid, memorable expression that also has a figurative use: removing or destroying something completely.
A typhoon is coming, and THE BLUE HEARTS sound thrilled about it. The chorus is just two lines shouted over and over: "台風が来る 景色が変わる" (a typhoon is coming, the scenery is changing) and "台風が来る 記録破りだ" (a typhoon is coming, it's record-breaking). It is short, loud and simple, which is exactly the point.
The storm is so huge that even "気象衛星「ひまわり」でさえ" (even the weather satellite "Himawari") can't track it. Himawari ("sunflower") is the real name of Japan's weather satellites, the ones behind every TV weather map there, so it's a fun local detail. The typhoon knocks down "古い大木" (old, big trees) and blows them away "根こそぎ" (roots and all), and it's described like a criminal: faster on its feet than a thief ("泥棒よりも速い逃げ足") and pushier than a robber ("強盗よりも強引なやつ").
Then the song sneaks in a jab at people. While the storm hits, "情報やデマが飛び交う" (information and false rumors fly around) and "声のでかい奴が笑う" (the guys with the loudest voices laugh). デマ (dema) means a false rumor, and でかい is a casual, slangy word for "big". You can hear the typhoon as a real storm, or as anything that shakes up how things look, while the noisiest people talk over everyone.