Special features of the diamond deposit named after M. V. Lomonosov are characterized, the deposit rocks being substituted by clayey minerals, mostly by saponite. Saponite properties are described: ability to swelling, high content of fine particles smaller than 5-10 microns, extremely low settling rate of particles. Problems of fine-dispersed clayey minerals dewatering are elucidated, and a method for consolidation and clarification of practically non-settling tailings slurry at OAO «Severalmaz» tailings storage facility is proposed.