The sample of IRAS galaxies with spectral energy distributions that peak near 60 microns are called Sixty Micron Peakers (SMPs or 60PKs). Their generally peculiar and amorphous morphologies, hot dust and lack of a cirrus component have been interpreted as being indicative of a recent interaction/merger event. Mid-infrared spectra of eight SMPs, obtained with ISOPHOT-S in the ~2-11 micron band are presented. Four of the observed sources are H II region-like (H2) galaxies, three are Seyfert 2 and one is unclassified. Emission attributed to Polycyclic Aromatic Hydrocarbons (PAHs) at 6.2, 7.7 and 8.6 micron is ubiquitous in the spectra. The PHOT-S spectrum of the H2 galaxy IRAS 23446+1519 exhibits a bright 11.04 micron line and an 8.6 micron feature of comparable size to its 7.7 micron feature. [S IV] emission at 10.5 micron was detected in three of four H2 galaxies and in one Seyfert 2 galaxy. The ratio of the 7.7 textmu m PAH feature to the continuum at 7.7 micron (PAH L/C) divides the eight SMPs at a ratio greater than 0.8 for H2 and less than 0.8 for Seyfert galaxies. An anti-correlation between PAH L/C and the ratio of the continuum flux at 5.9 micron to the flux at 60 micron is found, similar to that found in ultraluminous infrared galaxies. Silicate absorption at approximately 9.7 micron was observed in the Seyfert 2 galaxy, IRAS 04385-0828 and in IRAS 03344-2103. The previously unclassified SMP galaxy IRAS 03344-2103 is probably a Seyfert 2.