The Arduino Due does have a lot of hardware features that would assist your project. However very few of them are used in the standard Arduino libraries. To get the oscilloscope performance up to the million-samples-per-second class you would need to do a lot more than just analogRead().
If you're interested, download the datasheet and learn how to operate the ADC in DMA mode. You can also DMA the DAC. Or search for projects other people have published online. I'm sure there's a few.
The DAC on the Due is rather limited in its voltage output. Before starting with using the Due as an oscillator (signal generator) you should be sure that you can deal with its limited output. So you have to learn about opamps and analog circuitry too.
The Teensy has a better DAC (or two!) and much better library support for the advanced hardware features. For example, look at FrequencyTimer2 library which is included in the TeensyDuino library package. That may solve your oscillator problem right there.