Range-dependent clutter suppression poses significant challenges in airborne frequency diverse array (FDA) radar, where resolving range ambiguity is particularly difficult. Traditional space-time adaptive processing (STAP) techniques used for clutter mitigation in FDA radars operate in the physical domain defined by first-order statistics. In this paper, unlike conventional airborne uniform FDA, we introduce a space-time-range adaptive processing (STRAP) method to exploit second-order statistics for clutter suppression in the newly proposed co-pulsing FDA radar. This approach utilizes co-prime frequency offsets (FOs) across the elements of a co-prime array, with each element transmitting at a non-uniform co-prime pulse repetition interval (C-Cube). By incorporating second-order statistics from the co-array domain, the co-pulsing STRAP or CoSTAP benefits from increased degrees of freedom (DoFs) and low computational cost while maintaining strong clutter suppression capabilities. However, this approach also introduces significant computational burdens in the coarray domain. To address this, we propose an approximate method for three-dimensional (3-D) clutter subspace estimation using discrete prolate spheroidal sequences (DPSS) to balance clutter suppression performance and computational cost. We first develop a 3-D clutter rank evaluation criterion to exploit the geometry of 3-D clutter in a general scenario. Following this, we present a clutter subspace rejection method to mitigate the effects of interference such as jammer. Compared to existing FDA-STAP algorithms, our proposed CoSTAP method offers superior clutter suppression performance, lower computational complexity, and enhanced robustness to interference. Numerical experiments validate the effectiveness and advantages of our method.