go to https://www.twitch.tv/your-username/manager/highlights, and enter the following into the developer console (F12)

delete-twitch.js

// delete all twitch video highlights
for(var i = 0; i < document.getElementsByClassName("balloon__link--alert").length; i++) {
  var toDelete = document.getElementsByClassName("balloon__link--alert")[i]
  if (toDelete) {
    toDelete.click();
  }
  document.getElementsByClassName("button button--alert")[0].click()
}