Strange Waveform Using FPGA with NI myDAQ
Why is the input voltage dropping by almost 1V when the myDAQ is connected and why is the output wave dropping even lower than that?

You haven't said what circuit or instrument is generating the input signal, so there's no way we can know that.

The original signal was 3Vpp so shouldn't the output be the same?

When you pass the signal into the FPGA it will be fully digitized. Any analog features in the signal (ripple on the high or low level, the actual voltage of the high and low levels, rise and fall times of the edges, etc) will not be reflected in the output.
The output voltage levels will depend on what IO standard you chose for the FPGA output buffer. They can be totally unrelated to what voltage levels and IO standard you used for the FPGA input.