It seems that you must re-draw the canvas to clear the plot:
def Clear(self):
self.ui.widget.canvas.ax.clear()
self.ui.widget.canvas.draw()
self.ui.widget_2.canvas.ax.clear()
self.ui.widget_2.canvas.draw()
self.ui.widget_3.canvas.ax.clear()
self.ui.widget_3.canvas.draw()
self.ui.widget_4.canvas.ax.clear()
self.ui.widget_4.canvas.draw()