  An additional scalar degree of freedom for a gravitational wave is often
predicted in theories of gravity beyond general relativity and can be used for
a model-agnostic test of gravity. In this letter, we report the direct search
for the scalar-tensor mixed polarization modes of gravitational waves from
compact binaries in a strong regime of gravity by analyzing the data of
GW170814 and GW170817, which are the merger events of binary black holes and
binary neutron stars, respectively. Consequently, we obtain the constraints on
the ratio of scalar-mode amplitude to tensor-mode amplitude: $\lesssim 0.20$
for GW170814 and $\lesssim 0.068$ for GW170817, which are the tightest
constraints on the scalar amplitude in a strong regime of gravity before
merger.
