Garbage collection (GC) in log-structured file systems (LFS) is known to cause performance degradation, particularly in write-intensive scenarios. Existing approaches, such as in-storage migration and hotness-based grouping, aim to enhance GC efficiency. However, these approaches lack effective host-device collaboration, leading to either excessive communication overhead from inefficient task offloading or severe write amplification due to the log-on-log issue. We present CSGC, a host-device collaborative GC approach that utilizes computational storage device (CSD) to optimize GC efficiency. CSGC uses a pipelined CSD-offloaded migration framework with metadata piggybacking to reduce host-device communication overhead, along with a separate flash translation layer (sFTL) to preserve data hotness and mitigate write amplification. Our evaluations using F2FS and Daisy+ OpenSSD show that CSGC significantly improves GC performance, contributing to up to 3.6 \(\times \) and 1.9 \(\times \) speedup in I/O throughput over vanilla F2FS and IPLFS respectively.