Uh... the real answer, as sharke was wisely alluding (because he is familiar with sample based mashup music) is...
It depends.
Sonar is fully able to analyze, process and allow you to take an mp3 file and treat it like a wave. Obviously the higher quality the mp3 the better so if you have choice go for the higher quality mp3 (or even better try to get a cd quality or above wave file). Just mentioning that because perhaps the fact it's an mp3 is part of your question. Sonar can handle mp3's and convert them to/treat them like a proper wave is the point.
The other MAJOR factor is the material itself. If it is a rather sparse mix and a rather simple drum beat your chances of getting a useable beat extraction from a mixed song is much higher. That means if there are more instruments burying the drum part it's going to be harder to isolate the drum part (if not impossible).
If the drum part is really busy/fast with lots of fills and other craziness or is really dynamic (lots of loud and quiet parts like a jazz song) or poorly defined in the mix (like the kick, snare and other elements don't "CRACK" through to create a strong defined transient) then again it's going to be more difficult (or impossible) to yank it out in any useable way.
A straight up beat that can be heard clearly in "sparse" mix that does not bury the drum hits (and for this discussion you'll want to use the term "transients" but those don't apply specifically to drum hits... they are just volume spikes in an audio file that allows various things like "transient" detection to happen) is actually pretty easy to get a useable sample from or any of the other things one might do in this scenario.
So a strong, simple, defined drum beat with only some ambient keyboards or light vocals... pretty easy. A Slayer beat slathered with distorted guitars and screamer vocals... not so much.
People have been yanking beats from mixed material for a couple decades now but there is a skill to it.
You can eq out all the other elements focusing in on specific kit peices on multiple tracks then mix them back together. Like do a "badpass" EQ to focus in on the kick drum (maybe do two tracks to capture the "low" thud of the kick and the "beater" sound for the kick attack). On another track do the same thing to capture the snare "crack" (and maybe another to get the next resonant frequency down so you can mix the crack and meat of the snare together). The higher frequency stuff like cymbals, ride, hihat are trickier but a good strong hi hat in a sparse mix can again be focused in on with an eq. Toms are generally going to be a mess and best avoided but you can try (they'll be closer to your kick and lower snare freqs).
On a fully mixed track as well there will panning considerations. Like the hi hat will be off center. Kick will be centered. Snare may be slightly of to one side... crap like that. That's where effects/programs like R-Mix can be useful which allow you to hone in to not only the lo to high frequency range but where in the stereo field those sounds are occuring (so if your snare is off to the left a little you can adjust the frequency range to get at the hit frequency but also isolate it in the stereo field/reject whatever may be occupying the same frequncy range on the right side of the stereo field).
From a full stereo mix there will almost always be some bleed of the other sounds (and how much is dependent on how busy/congested the track is). A lot of that will be buried underneath any new sounds you add (so you have your backbeat that you have carefully yanked from the source and mixed back together and then you add your new instruments overtop of that which will, hopefully, mask the bleed from the original parts).
Then you beef up your surgically extracted kit peices with compression, EQ, limiters, reverb, saturation, etc so they aren't as thin (because you will have remove a LOT of the resonant frequencies with the bandpass EQ stuff).
That is old school grunto shiz.
Now we have fancy "replacement" tools like Sonar Drum Replacer and the older Audiosnap (and a bunch of other tools... and even more third party options) that can detect the "transients" (the drum hits) of your audio, convert the hits to MIDI notes and then feed them into drum sampling software to play back nice, big fat full sounding samples that haven't been carved to sh*t (which we did with the bandpass eqing).
Again these can be fiddly tools and require relatively clean, simple, clearly defined beats to be useable but are a LOT better than the old school crap. They also work a lot better though using material that has been isolated like I described earlier. So using a bandpass EQ to hone in on the transients of the kick, then using something like Drum Replacer to detect each hit (and feeding it into a drum sample program or just loading a sample into the Drum Replacer), then the Snare, and then the Hats, etc is a really cool way to do this.
You can then use your original, bandpassed, old school extracted beat and blend it in with your souped up, powerful drum sampler version to get the best of both worlds (like a parallel effect). Even just using kick samples mixed in to the original beat can have a dramatic effect.
You will also want to consider all the time stretching/groove clip looping stuff to take your new beats and use them at various tempos for original material or to match other sampled loops (which I'm assuming is part of the workflow you are going for).
Cheers.