I don’t know how Mazda measure the differential pressure in DPF to measure how much soot collected in DPF. If you remove the DPF without changing the configuration (disable the DPF) in the ECU, the ECU may give an error code.
if you can remove the DPF, it’s better to remove also the EGR system and disable the EGR in the ECU configuration also.
EGR system is to reduce cylinder temperature to reduce Nox, because nox generated when the cylinder temperature is very high. The side effect with EGR is the particulate matter will increase that is why the DPF is there to filter the exhaust gas.