After doing some digging and a little bit of research it turns out that Clarksdale did in fact have a minor league baseball team at one point! In fact Clarksdale had quite a rich history of baseball in the early part of the 20th century.
Baseball in Clarksdale started in 1904 when Clarksdale had a team in the 'Delta League'. That team lasted only one year until 1913 when the Clarksdale ball club started up again under the name "Swamp Angels" and played in the Cotton State League and lasted again only one season.
In 1921 Clarksdale played host to another professional ball team. This time they were known as the Clarksdale Cubs and played for three seasons before folding.
From 1924 to 1933 there is much less information on Clarksdale baseball because there was a lack of a professional team though independent baseball was still played between the cities of the Delta.
This is a photo of the 1925 Clarksdale independent baseball team. The article that accompanied this photo was from a 1926 paper that ran an article that discussed the schedule of the Clarksdale team as it was being formed. Apparently the schedule was a flexible affair as at press time of the article the name of the opposing team was not yet known but upcoming games against Lexa, AR and Cleveland, MS were discussed.
That was the last I could find about Clarksdale baseball until 1934 when a team from Louisiana decided to relocate to Clarksdale and called themselves the Clarksdale Ginners. This was a return to professional baseball for the town.
The Clarksdale Ginners drew 40,000 fans in their first season in Clarksdale, MS. Only two other ball clubs in the Cotton States pulled a larger crowd (being Pine Bluff, AR and Greenville, MS). Though the Ginners seemed to start well they were never able to finish strong due to injuries and other "unsurmountable obstacles" and never seemed to fare well by the end of the season.
The Clarksdale Ginners changed their name to the Clarksdale Planters and had an affiliation with the Cleveland Indians for the 1936 season and in 1938 began a two year relationship with the Boston Red Sox in which they changed their name to the Clarksdale Red Sox. The team even kept this name in '39 and '40 after the affiliation had ended.
1941 saw a return to the name Clarksdale Ginners and a season that ended at 48 wins and 88 losses. After that professional baseball left Clarksdale until 1947 when Clarksdale re-entered the Cotton States League where it remained until 1951.
Over the decades that Clarksdale had a professional baseball team, the town was in a baseball frenzy. Though the team never appeared to do very well statistically and never won a pennant, the town rallied around their team that was "characterized by swashbuckling baseball that was no less thrilling because it was usually not successful."
Several players from the Clarksdale teams either played in the major leagues before coming to Clarksdale or left to join major league teams including (*deep breath*): Harry Kane, Beals Becker, Clarence Kraft, John Merritt, Claude Thomas, Happy Foreman, Earl Webb, Bill Marshall, Doc Land, Otis Brannan, Fred Johnson, Oscar Tuero, Jim Pruett, Chet Morgan, Bill Henry, Bill Tremel, Dave Short, Calvin Chapman, Walter Brown, Bob McNamara, Thurman Tucker, Andy Gilbert, Randy Heflin, Bob Daughters, Mickey Harris, Red Barnes, Bob Finley, Alex Monchak, Woody Rich, Bill Nagel, Bill McGee, Jack Hallett, Josh Billings and Dino Chiozza.