The key point to realize is that for a diode mixer to operate properly, the LO must be much larger than the RF (at least 20 dB), and ideally much larger than the turn on voltage of the diodes. If this is true, then as a simplification consider the diodes to be ideal switches that are controlled solely by the amplitude of the LO. The time domain waveform at the IF is the RF signal multiplied by 0 or 1 depending on the state of the switches (which are switching at the LO frequency). It is a "chopped" version of the incident RF waveform. This produces the sum and difference frequencies, RF feedthrough, and a host of other harmonics. The IF filter then rejects all but the desired IF (upper or lower sideband). LO feedthrough at least is is not an issue in an ideal SBM, although it is there at a low level when actual components are used.