Multilingual machine translation models often outperform traditional bilingual models by leveraging translation knowledge transfer. Recent advancements have led to these models supporting hundreds of languages and achieving state-of-the-art results across various translation directions. However, as these models grow larger, their inference operations become increasingly costly. In many use cases, there is no need to support such a wide range of language pairs, as translation is typically needed in only a few selected directions. In this paper, we present CULL-MT, a compression method for machine translation models based on structural layer pruning and selected language directions. Our approach identifies and prunes unimportant layers using a greedy strategy, then mitigates the impact by applying knowledge distillation from the original model along with parameter-efficient fine-tuning. We apply CULL-MT to the NLLB-3.3B and LLaMA3.1-8B-Instruct models. In a multi-way translation scenario (Persian, French, and German to English), we find the NLLB-3.3B model to be robust, allowing 25% of layers to be pruned with only a 0.9 spBLEU drop. However, LLaMA3.1-8B-Instruct is more sensitive, with a 2.0 spBLEU drop after pruning 5 layers.