And it can spread mortar too!
The robot in this video was developed in Singapore by Future Cities Laboratory in collaboration with Swiss firm ROB Technologies AG.
It can set field tile twice as fast as a human, though it requires a human tender to mix mortar, grout, and cut and install anything that is not a full tile.
It is not shown in the video, but the suction cup attachment can be removed and replaced with one that extrudes mortar onto the substrate. There would typically be at least two robots on site, one to spread mortar and the other to set tile.
It makes sense that this would be used on commercial projects with vast expanses of tile; its developers expect it to be used for residential work too.