There are two effects occurring here:
Your liquid is evaporating, and
There is a capillary effect due to the adhesive property of water that lets water cling onto the side of your mug. It's the same effect that makes a meniscus.
So these two effects combined actually drives a current in your solution that brings these suspended particles to the cup, at the level of the coffee (i.e., the contact line), and the particles are deposited there when the water evaporates.
When seen in a droplet evaporating on a surface, this is also known as the coffee ring effect, and is frequently cited in literature because it can separate particles based on particle size as well, so can be used in nano-scale chromatography such as separating proteins, micro-organisms, and mammalian cells.