We present three-dimensional (3D) simulations of supernova explosions of nonrotating stars, triggered by the delayed neutrino-heating mechanism with a suitable choice of the core-neutrino luminosity. Our results show that asymmetric mass ejection caused by hydrodynamic instabilities can accelerate the neutron star (NS) up to recoil velocities of more than 700 km s-1 by the “gravitational tug-boat mechanism”, which is sufficient to explain most observed pulsar space velocities. The associated NS spin periods for our nonrotating progenitors are about 100 ms to 8000 ms without any obvious correlation between spin and kick magnitudes or directions. This suggests that faster spins and a possible spin-kick alignment might require angular momentum in the progenitor core prior to collapse. Our simulations for the first time demonstrate a clear correlation between the size of the NS kick and anisotropic production and distribution of heavy elements created by explosive burning behind the shock. In the case of large pulsar kicks, the explosion is significantly stronger opposite to the kick vector. Therefore the bulk of the explosively fused iron-group elements, in particular nickel, are ejected mostly in large clumps against the kick direction. This contrasts with the case of low recoil velocity, where the nickel-rich lumps are more isotropically distributed. Explosively produced intermediate-mass nuclei heavier than 28Si (like 40Ca and 44Ti) also exhibit significant enhancement in the hemisphere opposite to the direction of fast NS motion, while the distribution of 12C, 16O, and 20Ne is not affected, and that of 24Mg only marginally. Mapping the spatial distribution of the heavy elements in supernova remnants with identified pulsar motion may offer an important diagnostic test of the kick mechanism. Unlike kick scenarios based on anisotropic neutrino emission, our hydrodynamical acceleration model predicts enhanced ejection of iron-group elements and of their nuclear precursors in the opposite direction to the NS recoil.