Why does stall speed decreases with increasing aspect ratio?
$c_{L_{max}}$ doesn't change with changing AR. Is it true?


No, it isn't. Since the area near the wingtips cannot produce a pressure difference as large as that on the center wing due to flow around the wingtips, the lift there is reduced. The larger the wingtip part is relative  to the whole wing, the lower the maximum lift will be. 

Given the same wing area and mass, a wing with a higher aspect ratio will produce a lower stall speed. Of course, the assumption of an identical mass means that the lower aspect ratio wing has a poorer structural design.