You need to switch the "focus" of the commands to the editor. The way it's written now, it's trying to apply the "Select" command to the object in the object window.
Try:
Read from file: "sound.wav"
selectObject: "Sound sound"
Edit
editor Sound sound
Select: 0.108, 0.112
Extract selected sound (preserve times)
endeditor
selectObject: "Sound untitled"
Rename: "new sound"
NOTE: In the latest version of Praat for Windows (5.4.12), extracted sounds are automatically named "Sound untitled", hence the penultimate line. You might want to check in your version what the default name is for an extracted sound.
EDIT: Following @jja's suggestion, here is a revised version that uses an object ID to refer to the sound (I also replaced 'endeditor' with 'Close' so that it actually closes the editor window, and I dispensed with the selectObject command because I realized that the extracted sound object will already be selected):
sound = Read from file: "sound.wav"
selectObject: sound
Edit
editor: sound
Select: 0.108, 0.112
Extract selected sound (preserve times)
Close
Rename: "new sound"
As @jja points out, the use of an object ID is more robust because it guarantees that you are selecting the exact sound you read in; with the first method, if you have multiple objects with the same name in the object window you might select the wrong one.
Following @robert's suggestion, here is an alternative that bypasses the editor window (the manual way to access the "Extract part" command is to highlight the sound in the object window and choose Convert > Extract part...):
Read from file: "sound.wav"
selectObject: "Sound sound"
Extract part: 0.108, 0.112, "rectangular", 1, "yes"
selectObject: "Sound sound_part"
Rename: "new sound"