Deep metabarcoding offers an efficient and reproducible approach to biodiversity monitoring, but noisy data and incomplete reference databases challenge accurate diversity estimation and taxonomic annotation. Here, we introduce a novel algorithm, NEEAT, for removing spurious operational taxonomic units (OTUs) originating from nuclear-embedded mitochondrial DNA sequences (NUMTs) or sequencing errors. It integrates 'echo' signals across samples with the identification of unusual evolutionary patterns among similar DNA sequences. We also extensively benchmark current tools for chimera removal, taxonomic annotation and OTU clustering of deep metabarcoding data. The best performing tools/parameter settings are integrated into HAPP, a high-accuracy pipeline for processing deep metabarcoding data. Tests using CO1 data from BOLD and large-scale metabarcoding data on insects demonstrate that HAPP significantly outperforms existing methods, while enabling efficient analysis of extensive datasets by parallelizing computations across taxonomic groups.