A spokesman for the group said there was little other reason for Jones' departure than "it being time to move on".
During his tenure, Jones oversaw the transformation of John Mansfield Group into Communisis, spearheading last year's massive 250m, 10-year deal to print statements for HSBC.
Communisis said it was unable to give a timescale on Jones' replacement, but said "getting the perfect candidate will be what drives the speed of the selection process".
Jones will continue in the role for the foreseeable future until a replacement is found.
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