In this paper, we present a practical partitioned intelligent-reflecting-surface-aided transmit spatial modulation (PIRS-TSM) scheme, where spatial modulation is implemented at the transmitter and partitioning is conducted on the IRS to enhance the spectral efficiency (SE) and reliability for multiple-input single-output (MISO) systems. The theoretical analysis of average bit error rate (ABER) based on maximum likelihood (ML) detection and the computational complexity analysis are provided. Experimental simulations demonstrate that the PIRS-TSM scheme obtains a significant ABER enhancement under the same SE compared to the existing partitioned IRS-aided transmit space shift keying or generalized space shift keying schemes by additionally carrying modulated symbols. Moreover, the system performances with different configurations of antenna numbers and symbol modulation orders under the same SE are investigated as a practical application reference.