The Cut Text item is available via the Insert and Extract Text button on the collection toolbar, except when the Recycle Bin tab is active.
Select the Cut Text item to place the selected part of the text of the active clip onto the Windows clipboard. That selected part is then deleted from the clip. You can also cut text by pressing Ctrl+X on the keyboard while editing the clip's text.
See Editing Clips and Text to learn how to use AceText.