A cleaning composition that can discharge the color of blood, menstrual fluids, or other organic stains is provided. In particular, the present invention achieves a balance between control of unwanted liquid spreading by lateral wicking on a stained textile fabric to lessen the size of wet spots and maintaining the cleaning efficacy of the composition by means of specific kinds of thickening agents. The composition includes an oxidizing agent such as peroxides, a cell-lysing agent, a chelating agent, an antioxidant, a thickener, and other optional ingredients that are selectively employed to achieve an aqueous based composition that exhibits good shelf stability and stain removal properties. The thickening agent may include a cellulosic or clay material, starch, gum, fatty acid, fatty alcohol, hydrophilic colloidal particles, polyoxyethylene glycol or polyoxyethylene glycol derivatives including fatty acid esters and ethers, or a combination thereof.