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In this article we present the three-body fragmentation dynamics of ${\mathrm{C}}_{2}{{\mathrm{H}}_{4}}^{3+}$ caused by $18\text{\ensuremath{-}}\mathrm{keV}/\mathrm{u}\phantom{\rule{0.16em}{0ex}}{\mathrm{Ne}}^{8+}$ ion impact. Utilizing the cold target recoil ion momentum spectroscopy, the complete kinematical information of three fragmentation channels, i.e., ${\mathrm{C}}_{2}{{\mathrm{H}}_{4}}^{3+}\ensuremath{\rightarrow}{\mathrm{H}}^{+}+{\mathrm{H}}^{+}+{\mathrm{C}}_{2}{{\mathrm{H}}_{2}}^{+}, {\mathrm{H}}^{+}+\mathrm{C}{\mathrm{H}}^{+}+\mathrm{C}{{\mathrm{H}}_{2}}^{+}$, and ${\mathrm{H}}^{+}+{{\mathrm{H}}_{2}}^{+}+{\mathrm{C}}_{2}{\mathrm{H}}^{+}$ is obtained. For each channel, both concerted and sequential fragmentation mechanisms are observed and differentiated through the momentum correlation of resultant fragments visualized by the Dalitz plot and the Newton diagram. In particular, for the channel ${\mathrm{C}}_{2}{{\mathrm{H}}_{4}}^{3+}\ensuremath{\rightarrow}{\mathrm{H}}^{+}+{\mathrm{H}}^{+}+{\mathrm{C}}_{2}{{\mathrm{H}}_{2}}^{+}$, it is found in addition to the sequential pathway that the two protons can be emitted concertedly in two ways, i.e., from the same carbon atom or from the two carbon atoms. The present results show a more diverse molecular fragmentation triggered by ion collisions in contrast to a previous study using intense laser field ionization.