Digital synthesizer's like NI Massive, use wavetable samples for their oscillator tones. From there on you can use many different envelopes/filters/inserts/ etc to create a tones. Is there a DAW synthesizer that allows you to use your own sample for the wavetable to begin with on an oscillator? I don't mean create your own waveform, I mean use an audio sample. Thank you.
Camel Audio Alchemy does this very well. NI Absynth will also. Those are good to start with as well.
It sounds like what you're really asking for is more of an advanced sampler/rompler, but I'll mention a few that can work for what you're asking for.
The first two assume you have Logic:
1) Firstly, have you tried Logic's EXS24? It's extremely powerful... You can import whatever samples you want, assign a single one across the entire oscillator, or multiple ones across zones, or stack them. You have powerful control over whether samples loop, one-shot, reverse, and so on (and there's a built-in sample editor for trimming samples etc which tie in to regions). Then you have your usual synthesizer stages after that–filter, envelopes, and a powerful matrix in the center that allows for manipulating sounds for pretty good sound design capability. This synth is really in essence the closest thing to what you are asking for, I believe.
2) While it's oriented towards drums (since it has a built in sequencer), it can be used as a standalone synth, since you trigger the notes via midi – Logic's Ultrabeat will allow you to do what you want. It is a three oscillator system where one oscillator is simply a sample that you select, and can route into filtering and enveloping from there. The other two oscillators are a regular generated oscillator and a noise oscillator, and each can be turned on and off, so they are optional.
3) NI's Battery, while also set up for drums, can be used as a normal synth, and is totally based around samples.
4) If using Ableton, this is like EXS24; you drop in a sample, and it's in the sampler instrument, which has synth like stages. Not as advanced as EXS24, but still, fits the bill.
5) If you really want to get creative, Waves's Codex synthesizer is pretty incredible. It's wavetable-based and you can import your own samples (which are the only samples used). You just initialize a patch and you have two oscillators, and you hit import, and import your sample(s) (you can have two simultaneously). The sample will be pitch-detected and turned into a wavetable. You can then change the start/end/formant settings. But the beauty of this synth is it's ability to use the samples as graintable samples (looping slices of them) so keep that in mind (it's intended to make radically new sounds of out of the samples, not simply trigger samples); though it can in theory simply play the samples as one shots. Maybe check out the demo if considering this one.