This paper presents two methods for blind carrier frequency offset (CFO) estimation for amplitude phase shift keying (APSK) signals. The first approach carries out modulation removal using the outermost symbols of APSK and then utilizes an iterative parabolic interpolation technique to mitigate the bias of FFT-based CFO estimation. The second method conducts two-stage full modulation removal and aggregates symbols to reduce the FFT size for CFO estimation. In the symbol aggregation process, modulation-removed symbols are paired and weighted based on their reliability to achieve accurate estimation. The first method demonstrates better performance, particularly for high-precision requirements, while the second method offers a more adaptable trade-off between performance and complexity by adjusting the aggregation length. Both methods are more efficient and provide better mean square error (MSE) performance compared to existing ones. Moreover, numerical complexity analyses show the efficiency of the proposed algorithms.