Any process in which a virus stops, prevents, or reduces the frequency, rate or extent of host STAT1 (signal transducer and activator of transcription-1) activity by the removal of phosphoric residues from STAT1-O-phospho-tyrosine to form STAT1-tyrosine. For example, the viral phosphatase VH1 dephosphorylates STAT1 to reverse STAT1 activation.