Reply to Digital v Analogue summing and distortioin

Ez all,
I have a curiosity that's been bugging me for a while, hopefully someone here can put me straight.

If I mix two digital music sources externally using a traditional analogue mixer (i.e. DVS setup) and clip the signal on the mixer and only on the mixer, am I clipping the signal as analogue or digital?

The reason I ask is I hear much uproar about clipping a digital signal due to the way that type of sound degrades. But then an analogue signal clips differently, some people citing a more harmonic distortion instead of square waves produced by digital.

As a digital guy in a sea of analogue I find my vinylist counterparts often clip channel signals and potentially even the master out. My digital gear is set so the internal gain structure does not clip, this however means my music is generally much quieter than my analogue cousins. This is usually rectified by a swift bump of the master. But sometimes I have no more headroom on the mixer and the previous DJ has rinsed the gains, the sound man is getting a BJ and I need moar power! The only way to match the volume and keep the vibe is to also, rinse the gains.

If I am correct, mixing externally in this fashion should also create the same 'harmonic distortion' effect as traditional analogue simply because of the DAC's on the soundcard (which are not being clipped) at the start of the signal chain.
Am I right?