An experimental study of self-Q-switching (SQS) in an ytterbium doped fiber laser (YDFL) arranged using a twin-core GTWave assembly is reported. The main mechanisms that initiate, amplify, and limit SQS pulses in amplitude are revealed to be stimulated Brillouin and Raman scattering (SBS/SRS) and Yb3C amplified spontaneous emission. The parameters featuring SQS oscillation in terms of efficiency and stability of pulsing are found to be intra-cavity loss and feedback strength. An analysis of the YDFL SQS regime’s features—pulsing time series, optical and RF spectra, amplitude and timing jitter—is provided for the two experimental situations: (i) when SQS pulsing stochastically intermits with regular active Q-switching pulses, given by the action of an intra-cavity acousto-optical modulator, and (ii) when a pure SQS mode is intentionally implemented in the YDFL without a modulator. The close relationship of the processes involved and SQS parameters in these two circumstances is demonstrated. Giant pulses with durations of 70–80 ns are shown to be generated at threshold intra-cavity powers of around 250 W (SBS threshold) and limited at approximately 2 kW of peak power (SRS threshold). At SBS-SQS, we show that at high values of intra-cavity loss, and thus reduced feedback, the amplitude and timing jitter values can be reduced to 5% and 7%, respectively.