Please provide minimal code example of Sprite following the mouse in Godot. There are complex and big sample projects, but I didn't found nothing small and clear.
Put the Sprite
node in the scene, and attach the following script to it.
const SPEED = 500
func _process(delta):
var vec = get_viewport().get_mouse_position() - self.position # getting the vector from self to the mouse
vec = vec.normalized() * delta * SPEED # normalize it and multiply by time and speed
position += vec # move by that vector