3D Gaussian splatting (3DGS) has emerged as a promising direction for SLAM due to its high-fidelity reconstruction and rapid convergence. However, 3DGS-SLAM algorithms remain impractical for mobile platforms due to their high computational cost, especially for their tracking process. This work introduces Splatonic, a sparse and efficient realtime 3DGS-SLAM algorithm-hardware co-design for resourceconstrained devices. Inspired by classical SLAMs, we propose an adaptive sparse pixel sampling algorithm that reduces the number of rendered pixels by up to$256 \times$while retaining accuracy. To unlock this performance potential on mobile GPUs, we design a novel pixel-based rendering pipeline that improves hardware utilization via Gaussian-parallel rendering and preemptive$\alpha$-checking. Together, these optimizations yield up to$121.7 \times$speedup on the bottleneck stages and$14.6 \times$end-toend speedup on off-the-shelf GPUs. To further address new bottlenecks introduced by our rendering pipeline, we propose a pipelined architecture that simplifies the overall design while addressing newly emerged bottlenecks in projection and aggregation. Evaluated across four 3DGS-SLAM algorithms, Splatonic achieves up to$274.9 \times$speedup and$4738.5 \times$energy savings over mobile GPUs and up to$25.2 \times$speedup and$241.1 \times$energy savings over state-of-the-art accelerators, all with comparable accuracy.