US61 and US49 cross just outside Clarksdale -- that's one theory.

Another theory contends that it's an intersection of two *railroads,* not highways: "where the Southern cross the Dog." The "Dog" is the "Yellow Dog," a rail line whose real name I forget -- Yazoo Something-or-other, maybe; the "Southern" is the Illinois Southern, a north-south line connecting Chicago and New Orleans.

There's been at least one previous thread on this subject, with plenty of well-researched answers. Maybe we'll see a list of Related Threads atop this page if the topic stays alive long enough.