Formal specifications are essential to express precisely systems, but they are often difficult to define or unavailable. Specification mining aims to automatically infer specifications from system executions. The existing literature mainly focuses on learning properties defined on single system executions. However, many system characteristics, such as security policies and robustness, require relating two or more executions, and hence cannot be captured by properties. Hyperproperties address this limitation by allowing simultaneous reasoning about multiple executions with quantification over system traces. In this paper, we propose an effective approach for mining Hyper Signal Temporal Logic (HyperSTL) specifications. Our approach is based on the syntax-guided synthesis framework and allows users to control the amount of prior knowledge embedded in the mining procedure. To the best of our knowledge, this is the first mining method for hyperproperties that does not require a pre-defined template as input and allows for quantifier alternation. We implemented our approach and demonstrated its applicability and versatility in several case studies where we showed that we can use the same method to mine specifications both with and without templates, but also to infer subsets of HyperSTL, including STL, HyperLTL, LTL and non-temporal specifications.