This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered $n$-dimensional Clifford-valued systems into $2^{m}n$-dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis.