The process of magnetic relaxation was studied in bismuth ferrite BiFeO3 multiferroic micro-cubes obtained by means of microwave assisted Pechini process. Two different mechanisms of relaxation were found. The first one is a rapid magnetic relaxation driven by the domain reorientations and/or pinning and motion of domain walls. This mechanism is also responsible for the irreversible properties at low temperatures. The power-law decay of the magnetic moment confirms that this relaxation takes place in the system of weakly interacting ferromagnetic or superferromagnetic domains. The second mechanism is a longterm weak magnetic relaxation due to spin glass-phase.