Interseeding annual warm‐season forages into perennial cool‐season grasses may increase herbage mass and quality. Yet, methods to do so successfully remain elusive. From 2020 to 2022, we conducted an experiment that evaluated herbage mass responses to sod suppression after interseeding sorghum × sudangrass [Sorghum bicolor (L.) Moench × S. bicolor (L.) Moench ssp. drummondii (Nees ex Steud.) de Wet & Harlan] in three N‐fertilized and three mixed‐legume smooth bromegrass (Bromus inermis Leyss.) pastures. Sod suppression treatments included glyphosate [N‐(phosphonomethyl) glycine] applications of 0, 0.55, 1.10, 1.65, and 2.20 kg ha−1 on pastures that were heavily grazed in two rotational stocking periods in spring and an additional 0 kg ha−1 glyphosate control where herbage was stockpiled throughout spring, mowed, and removed before interseeding sorghum × sudangrass. In herbage samples collected 8 weeks after treatment, perennial grass mass showed exponential decay responses as glyphosate rate increased, while sorghum × sudangrass, weedy grass, and total herbage mass showed logistic growth responses. Sorghum × sudangrass reached a high of 2316 kg ha−1 as glyphosate rate increased to 1.65 kg ha−1 while weedy grass mass continued to increase as glyphosate rate increased to 2.20 kg ha−1. Reduced perennial grass mass in herbage samples collected the next spring indicated the presence of a tradeoff between increasing summer herbage now and reducing next spring herbage later with glyphosate application after interseeding sorghum × sudangrass. We concluded practitioners should not use glyphosate for sod suppression before interseeding warm‐season annual forages into perennial cool‐season grass pastures.