Large amounts of the waste SiC sludge containing small amounts of Si and organic lubricant were produced during the wire cutting process of the single silicon crystal ingots. The waste SiC sludge was purified by the washing process and the purified SiC powders were used to fabricate continuously porous $SiC-Si_3N_4$ composites using a fibrous monolithic process, in which carbon, $6wt\%;Y_2O_3-2;wt\%;A1_2O_3$ and ethylene vinyl acetate were added as a pore-forming agent, sintering additives, and binder, respectively. In the burning-out process, carbon was fully removed and continuously porous $SiC-Si_3N_4$ composites were successfully fabricated. The green bodies containing SiC, Si particles and sintering additives were nitrided at $1410^{circ}C$ in a flowing $N_2+10\%;H_2$ gas mixture. Continuously porous composites were combined with SiC, ${alpha}Si_3N_4,;eta-Si_3N_4$ and a few $\%$ of Fe phases. The pore size of the 2nd and the 3rd passed $SiC-Si_3N_4$ composites was $260;{mu}m$ and $35;{mu}m$ in diameter, respectively.