  We explore the effects of considering various infrared (IR) cutoffs,
including the particle horizon, Ricci horizon and Granda-Oliveros (GO) cutoffs,
on the properties of Tsallis holographic dark energy (THDE) model, proposed
inspired by Tsallis generalized entropy formalism \cite{THDE}. Interestingly
enough, we find that for the particle horizon as IR cutoff, the obtained THDE
model can describe the accelerated universe. This is in contrast to the usual
HDE model which cannot lead to an accelerated universe, if one consider the
particle horizon as IR cutoff. We also investigate the cosmological
consequences of THDE under the assumption of a mutual interaction between the
dark sectors of the Universe. It is shown that the evolution history of the
Universe can be described by these IR cutoffs and thus the current cosmic
acceleration can also been realized. The sound instability of THDE models for
each cutoff are also explored, separately.
