A joint communication and computation (JCC) framework using segmented pinching antenna system (PASS) is proposed, where both the communication bit streams and computation data are simultaneously transmitted via uplink communications. The segmented PASS design is used to yield the tractable uplink transmission, and to mitigate large-scale path loss and in-waveguide loss. Based on three operating protocols, namely segment selection (SS), segment aggregation (SA), and segment multiplexing (SM), the joint transmit and receive beamforming problem is formulated: 1) The mean square error (MSE) minimization problem is formulated for computation-oriented cases. To address this problem, a low-complexity alternating optimization-minimum mean square error (AO-MMSE) algorithm is developed. This problem is decomposed into receiver-side and transmitter-side MSE subproblems that are iteratively optimized by MMSE receivers to obtain the closed-form solutions. It is mathematically proved that the segmented JCC-PASS framework significantly outperforms the conventional PASS for the average in-waveguide propagation gain. 2) The weighted sum rate (WSR) maximization problem is formulated for communication-oriented cases. To solve the decomposed receiver-side and transmitter-side MSE subproblems, the AO-weighted minimum mean square error (AO-WMMSE) algorithm is further developed. An auxiliary weight variable is introduced to linearize the WSR function and is alternatively optimized based on WMMSE to derive the closed-form solutions. Simulation results demonstrate that: i) The proposed JCC-PASS framework achieves up to 70.65% and 45.32% reductions in MSE compared with conventional MIMO and conventional PASS, and ii) it reaches 87.70% and 51.35% improvements in WSR compared with conventional MIMO and conventional PASS, respectively.