The dawn of softwarized networks enables Network Slicing (NS) as an important technology towards allocating endto-end logical networks to facilitate diverse requirements of emerging applications in fifth-generation (5G) mobile networks. However, the emergence of NS also exposes novel security and privacy challenges, primarily related to aspects such as NS life-cycle security, inter-slice security, intra-slice security, slice broker security, zero-touch network and management security, and blockchain security. Hence, enhancing NS security, privacy, and trust has become a key research area toward realizing the true capabilities of 5G. This paper presents a comprehensive and up-to-date survey on NS security. The paper articulates a taxonomy for NS security and privacy, laying the structure for the survey. Accordingly, the paper presents key attack scenarios specific to NS-enabled networks. Furthermore, the paper explores NS security threats, challenges, and issues while elaborating on NS security solutions available in the literature. In addition, NS trust and privacy aspects, along with possible solutions, are explained. The paper also highlights future research directions in NS security and privacy. It is envisaged that this survey will concentrate on existing research work, highlight research gaps and shed light on future research, development, and standardization work to realize secure NS in 5G and beyond mobile communication networks.