Digital filter performance with noncontinuous signal?
It is not surprising that the filter output resembles the filter's step response at discontinuities of the input signal. It's like applying a (modulated) step at the input. Apparently the cut-off frequency of the high-pass filter is higher than the frequency of the sinusoid, so the output goes to zero after each discontinuity. However, at each point of a discontinuity, the input signal contains frequencies above the cut-off frequency of the high-pass filter and these frequencies are passed to the output.