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We focus on the ratio of ${\\cal R}(\\theta_c) \\equiv {\\cal B}( \\Xi_{cc} \\to \\Xi_c' e^+ \\nu_e)/ {\\cal B}( \\Xi_{cc} \\to \\Xi_c e^+ \\nu_e) $ and find that $({\\cal R}(\\theta_0),{\\cal R}(- \\theta_0)) =(0.46 \\pm 0.01,7.33 \\pm 0.23)$ with $\\theta_0 = 0.137\\pi$, which are in sharp contrast to ${\\cal R}(0)=2.15\\pm0.11$ without the mixing. The ratio is enhanced~(suppressed) by a factor of four for a negative~(positive) $\\theta_c$. 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