The memory function approach to spin dynamics in doped antiferromagnetic insulator combined with the assumption of temperature independent static spin correlations and constant collective mode damping leads to ω/T scaling in a broad range. The theory involving a nonuniversal scaling parameter is used to analyze recent inelastic neutron scattering results for underdoped cuprates. Adopting modified damping function also the emerging central peak in low-doped cuprates at low temperatures can be explained within the same framework.