Automatically detecting and removing Electroencephalogram (EEG) outliers is essential to design robust brain-computer interfaces (BCIs). In this paper, we propose a novel outlier detection method that works on the Riemannian manifold of sample covariance matrices (SCMs). Existing outlier detection methods run the risk of erroneously rejecting some samples as outliers, even if there is no outlier, due to the detection being based on a reference matrix and a threshold. To address this limitation, our method, Riemannian Spectral Clustering (RiSC), detects outliers by clustering SCMs into non-outliers and outliers, based on a proposed similarity measure. This considers the Riemannian geometry of the space and magnifies the similarity within the non-outlier cluster and weakens it between non-outlier and outlier clusters, instead of setting a threshold. To assess RiSC performance, we generated artificial EEG datasets contaminated by different outlier strengths and numbers. Comparing Hit-False (HF) difference between RiSC and existing outlier detection methods confirmed that RiSC could detect outliers significantly better (p < 0.001). In particular, RiSC improved HF difference the most for datasets with the most severe outlier contamination.