We address the problem of machine unlearning in neural information retrieval (IR), introducing a novel task termed neural machine unranking (NuMuR). This problem is motivated by growing demands for data privacy compliance and selective information removal in neural IR systems. Existing task-agnostic or model-agnostic unlearning approaches, primarily designed for classification tasks, are suboptimal for NuMuR due to two core challenges: 1) neural rankers output unnormalised relevance scores rather than probability distributions, limiting the effectiveness of traditional teacher-student distillation frameworks and 2) entangled data scenarios, where queries and documents appear simultaneously across both forget and retain sets, may degrade retention performance in existing methods. To address these issues, we propose contrastive and consistent loss (CoCoL), a dual-objective framework. CoCoL comprises 1) a contrastive loss that reduces relevance scores on forget sets while maintaining performance on entangled samples and 2) a consistent loss that preserves accuracy on the retain set. Extensive experiments on two datasets, across four neural IR models, demonstrate that CoCoL achieves substantial forgetting with minimal retention and generalization performance loss. CoCoL facilitates more effective and controllable data removal than existing techniques.