Viral pathogen can rapidly evolve, adapt to novel hosts and evade human immunity. The early detection of emerging viral pathogens through biosurveillance coupled with rapid and accurate diagnostics are required to mitigate global pandemics. However, RNA viruses can mutate rapidly, hampering biosurveillance and diagnostic efforts. Here, we present a novel computational approach called FEVER (Fast Evaluation of Viral Emerging Risks) to design assays that simultaneously accomplish: 1) broad-coverage biosurveillance of an entire class of viruses, 2) accurate diagnosis of an outbreak strain, and 3) mutation typing to detect variants of public health importance. We demonstrate the application of FEVER to generate assays to simultaneously 1) detect sarbecoviruses for biosurveillance; 2) diagnose infections specifically caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); and 3) perform rapid mutation typing of the D614G SARS-CoV-2 spike variant associated with increased pathogen transmissibility. These FEVER assays had a high in silico recall (predicted positive) up to 99.7% of 525,708 SARS-CoV-2 sequences analyzed and displayed sensitivities and specificities as high as 92.4% and 100% respectively when validated in 100 clinical samples. The D614G SARS-CoV-2 spike mutation PCR test was able to identify the single nucleotide identity at position 23,403 in the viral genome of 96.6% SARS-CoV-2 positive samples without the need for sequencing. This study demonstrates the utility of FEVER to design assays for biosurveillance, diagnostics, and mutation typing to rapidly detect, track, and mitigate future outbreaks and pandemics caused by emerging viruses.