In this work we study the weak decays of $$\Xi _{cc}\rightarrow \Xi _c$$ ${\Xi }_{\mathrm{cc}}\to {\Xi }_c$ and $$\Xi _{cc}\rightarrow \Xi '_c$$ ${\Xi }_{\mathrm{cc}}\to {\Xi }_c^{\prime }$ in the light-front quark model. Generally, a naive, but reasonable conjecture suggests that the cc subsystem in $$\Xi _{cc}$$ ${\Xi }_{\mathrm{cc}}$ ( us pair in $$\Xi ^{(')}_c$$ ${\Xi }_c^{{(}^{\prime })}$ ) stands as a diquark with definite spin and color assignments. During the concerned processes, the diquark of the initial state is not a spectator, namely must be broken. A Racah transformation would decompose the original (cc)q into a combination of c(cq) components. Thus we may deal with the decaying c quark alone while keeping the (cq) subsystem as a spectator. With the re-arrangement of the inner structure we calculate the form factors numerically and then obtain the rates of semi-leptonic decays and non-leptonic decays, which will be measured in the future.