The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes . In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution . Using high-speed imaging, we characterize the different stages of the detachment . Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity . In the viscoelastic regime, particles do not affect the thinning until the onset of the blistering instability, which they accelerate . We find that the transition from one regime to another, which corresponds to the coil-stretch transition of the polymer chains, strongly depends on the particle content . Considering that the presence of rigid particles increase the deformation of the liquid phase, we propose an expression for the local strain rate in the suspension, which rationalizes our experimental results . This method could enable the precise measurement of local stresses in particulate suspensions.