Sunspots are cooler than the surrounding solar surface because

Because the convection process stops and hotter plasma doesn't replace the cooler plasma on the surface

Explanation:

Sun spots are the darker and relatively cooler regions on the surface of the Sun (photosphere). Their temperature is around 1000° C lower than the Sun's surface.

Reason: The Sun's surface is granulated because of the convection process happening in the layer just below the photosphere. Because of the convection, hotter plasma comes on the surface, release energy, and then gets replaced by the hotter plasma. Just like tea or water boils. The places where magnetic field line enter into and exit from the surface, this convection process stops. Thus these area starts getting cooler and appear black in color.