  Let $f:X\to X$ be a non-isomorphic (i.e., $\text{deg } f>1$) surjective
endomorphism of a smooth projective threefold $X$. We prove that any birational
minimal model program becomes $f$-equivariant after iteration, provided that
$f$ is $\delta$-primitive. Here $\delta$-primitive means that there is no
$f$-equivariant (after iteration) dominant rational map $\pi:X\dashrightarrow
Y$ to a positive lower-dimensional projective variety $Y$ such that the first
dynamical degree remains unchanged. This way, we further determine the building
blocks of $f$. As the first application, we prove the Kawaguchi-Silverman
conjecture for every non-isomorphic surjective endomorphism of a smooth
projective threefold. As the second application, we reduce the Zariski dense
orbit conjecture for $f$ to a terminal threefold with only $f$-equivariant Fano
contractions.
