I am designing an active bandpass filter by cascading a low pass and a
high pass filter. I have been told that the stop band attenuation must
be at least -40dB/Decade.

If the both the low and high pass filter have a rolloff of
-20dB/Decade, does that mean that the resultant bandpass filter will
have a rolloff of -40dB/Decade?

Thanks

The high pass filter attenuates below the pass band and the low pass
filter attenuates above the pass band. Since they are cutting at
different frequencies, you don't have an additive effect. You would
need a 40dB high pass and a 40dB low pass to form a 40dB band pass.