Orthogonal frequency-division multiplexing (OFDM) techniques are promising for underwater acoustic (UWA) communications due to their robustness against large delay spread. However, OFDM systems in UWA channels suffer from intercarrier interference (ICI) caused by the Doppler effect. In this paper, we propose four low-complexity mirror-mapping-based ICI cancellation schemes in OFDM UWA communications without explicitly estimating ICI coefficients or carrier frequency offset (CFO), namely the mirror symbol repetition (MSR) scheme, the mirror conjugate symbol repetition (MCSR) scheme, the mirror conversion transmission (MCVT) scheme, and the mirror conjugate transmission (MCJT) scheme. We theoretically evaluate their performance by deriving their carrier-to-interference power ratio (CIR) expressions in multipath Rayleigh fading channels with CFO. The key idea of our proposed schemes is to employ data repetition within one or two consecutive OFDM symbols according to the mirror-mapping rules and apply the conjugate or conversion operations to remove ICI. Theoretical analyses and numerical results show that the proposed mirror-mapping-based schemes can effectively improve the CIR in comparison with the plain OFDM and the adjacent-mapping-based schemes. In addition, the effects of the channel length and the CFO deviation between two consecutive OFDM symbols are investigated. Finally, to demonstrate their benefits for OFDM UWA communications, these schemes have also been tested in a recent sea experiment conducted in Taiwan in May 2013. The decoding results validate that the proposed mirror-mapping-based schemes significantly improve the bit error rate (BER) performance of OFDM communications in UWA channels.