Sawdust joint is a term used to refer to the overall quality of a gambling establishment. The term joint is jargon used to refer to a building, but things get interesting once you add the word sawdust to the mix.
Namely, back in the day in some older casino establishments, casino owners used to sprinkle and cover hard wooden floors with sawdust, which is how the term was coined. They did that because sawdust was used to absorb spilled liquids and muffle the sound made by people walking on hard wooden floors.
An opposite term of sawdust joint is rug joint. As the name suggests, it refers to casino establishments that had carpets instead of sawdust and were considered to be more prestigious and luxurious than the sawdust ones.