Yes, mow it! Mowing works to at least prevent seed spread and regular mowing will weaken rhizomes.
Seed establishment has the greatest potential for the establishment and spread of johnsongrass and must be prevented. Therefore, mowing works to at least prevent seed spread. An individual plant can produce 28,000-30,000 seeds and a single inflorescence can measure 1,240 seeds (Keeley and Thullen, 1979). Viable seed may be produced as early as 2 weeks after flowering begins, so timely control measures throughout the season are needed to prevent seed production. Even though the viability of johnsongrass seed in soil remains high for as long as five years, seed can remain viable in soil up to 10 years.
Regular mowing can be effective in both orchard and non-crop situations. Due to its capacity to regenerate from rhizome fragments, complete control of S. halepense by mowing alone is difficult. Nonetheless, intensive grazing and mowing can be used to reduce a stand of johnsongrass. If grazed or mowed closely for at least two years, the plants become weak and stunted and the rhizomes become concentrated near the soil surface.
Consider mowing johnsongrass stands before seeds set to weaken current stands and avoid the spread through seed dispersal.
REFERENCE
P. E. Keeley, & R. J. Thullen. (1979). Influence of Planting Date on the Growth of Johnsongrass (Sorghum halepense) from Seed. Weed Science, 27(5), 554-558. Retrieved June 30, 2020, from www.jstor.org/stable/4043118