In elastic optical networks (EONs), the slicing-and-stitching technique has emerged as a promising solution to reduce spectrum fragmentation by breaking the subcarrier consecutiveness constraint. This physical layer technology enables all-optical slicing of requests, allowing them to be accommodated in multiple non-consecutive spectral slots within an EON. In this paper, we investigate the survivable routing problem in EONs with slicers. Specifically, we consider the dedicated path protection (DPP) scheme to address single edge failures. For each connection request, we aim to find a pair of link-disjoint lightpaths to route the request. Additionally, we propose four heuristic algorithms to determine the routing paths based on two different slicing schemes, namely source and L-shape. Through extensive simulations, we evaluate the performance of the proposed algorithms and demonstrate their effectiveness in achieving satisfactory results.