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Nanostructured TaS2 with different concentrations of intercalated Mn ions has been investigated using ac and dc magnetization measurements. The nanostructures are composed of tapes that are less than a micron wide, which themselves are comprised of tubular structures with an average diameter of about 100 nm. The sample with a concentration x=0.15 of Mn exhibited a transition from paramagnetism to a cluster glass state at approximately 8 K. The dynamics of this cluster glass state was better described by the Vogel–Fulcher–Tammann law than by critical slowing down, which suggests that the transition is not a continuous one. The cluster glass state exhibited aging-related memory, which is typically observed in canonical spin glasses and superspin glasses. The sample with x=0.23 underwent a paramagnetic to ferromagnetic transition at 85 K. Nonlinear susceptibility measurements suggest that there is another transition close to but somewhat lower than 85 K. With a small measuring field, both zero-field-cooled and field-cooled magnetizations exhibit peaks and dramatic downturns at low temperatures. The field-cooled magnetization also exhibits temperature hysteresis. The unusual behavior of the field-cooled magnetization is due to relaxation and cooling-rate effects. The overall behavior of nanostructured MnxTaS2 possesses the hallmarks of competition between clustered magnetic ground states in a disordered magnetic system.