A three-dimensional (3D) permute unit for a single-instruction-multiple-data stacked processor includes a first vector permute subunit and a second vector permute subunit. The first and second vector permute subunits are arranged in different layers of a 3D chip package. The vector permute subunits are each configured to process a portion of at least two input vectors. A first contact sub-field of the first vector permute subunit is configured to connect output ports of a first crossbar of the first vector permute subunit, holding an intermediate result of the first vector permute subunit, to a second contact sub-field of the second vector permute subunit. A first contact sub-field of the second vector permute subunit is configured to connect output ports of a first crossbar of the second vector permute subunit, holding an intermediate result of the second vector permute subunit, to a second contact sub-field of the first vector permute subunit.