To accomplish complex tasks, several nano-machines may need to communicate via multiple-access channel with one access point, where information fusion is carried out. However, multiple-access Diffusive Molecular Communications (DMC) systems suffer from severe Multiple-Access Interference (MAI) and Inter-Symbol Interference (ISI), which should be effectively mitigated at receiver in order to achieve acceptable performance. Built on two fundamental single-user detection schemes, namely Threshold assisted Majority Vote Detection (TMVD) and Equal Gain Combination Detection (EGCD), we first propose three low-complexity interference cancellation schemes, which are the TMVD-assisted Iterative Interference Cancellation (TMVD-IIC), TMVD-based Minimum-Distance Decoding assisted Interference Cancellation (TMVD-MDDIC) and the EGCD-assisted N-order Iterative Interference Cancellation (EGCD-NIIC), for operation in the Molecular Type Spread assisted Molecular Shift Keying (MTS-MoSK) DMC systems. Then, following the principle of maximum likelihood detection, we propose a Simplified Approximate Maximum Likelihood (SAML) detection scheme. The error performance of the MTS-MoSK DMC systems employing respectively the considered detection schemes is comprehensively investigated and compared. Furthermore, the complexities of the detection schemes are analyzed and discussed in terms of the complexity-performance trade-off. Our studies and results show that, compared with the single-user TMVD and EGCD schemes, the proposed interference cancellation schemes are capable of mitigating efficiently the effect of MAI and enabling significant performance improvement at the slightly increased complexity.