This is document lists the four iPod shuffle models and the ways to sync music to the shuffle.
The way you remove songs depends on the model (1st and 2nd gen versus 3rd and 4th gen), and the method being used to add songs. I don't know your specifics (please provide), I'll go with one possibility...
You have a 4th (current) gen shuffle and you use the manual method to load the shuffle, by dragging songs to the shuffle from your iTunes library in iTunes (or using the Autofill feature). If that is your shuffle model and how you load it...
First, in the latest iTunes, the sidebar can be hidden. To show it, go up to the menu bar, under View, and select Show Sidebar.
To remove songs, select the shuffle in the sidebar, under DEVICES. "Drop down" its content list, which is indented below the iPod. Click on Music there. Over to the right, you see a list of songs currently on the shuffle. Select the song you want to remove, and hit the Delete key on keyboard. Confirm action. You can do this with one song, a selection of songs, or the entire list (by selecting Select All from the File menu).
If you have a 1st or 2nd gen shuffle, or you use automatic syncing (not manual loading or Autofill), please post back.