A stellar system is dynamically hot when its kinetic energy is dominated by random motion represented by the velocity dispersion σhot. We use MaNGA data to obtain the inner and outer dispersion of a galaxy, σin and σout, to characterize its dynamical status and study its connection with star formation quenching and the growth of its supermassive black hole (SMBH). We divide galaxies into fully quenched (FQGs), partially quenched (PQGs), and fully star-forming (FSGs) populations, and identify quenched central cores (QCCs) in PQGs. The galaxy distribution in (σin/σhot)–(σout/σhot) diagram is L-shaped, consisting of a horizontal sequence (σout/σhot ∼ 0) and a vertical sequence (σin/σhot ∼ 1). FQGs and QCCs are located at the top of the vertical sequence, σout/σhot ∼ 1, and are thus dynamically hot over their entire bodies. PQGs reside along the vertical sequence, so they have hot centers but cold outskirts. FSGs are diverse and can be found in both sequences. Galaxy structural properties, star formation, and AGN activities make a transition along the horizontal sequence at σin/σhot ∼ 0.5, and along the vertical sequence at σout/σhot ∼ 0.5. The fractions of optical AGNs and barred galaxies increase rapidly in the first transition and decline rapidly in the second; radio galaxies are located at the top of the vertical sequence. Our results demonstrate that star formation quenching and SMBH growth are effective only in dynamically hot systems. A simple model along this line can reproduce the observed SMBH scaling relations. We discuss how secular processes and strong interactions can make a system dynamically hot, and lead to the SMBH growth and star formation quenching.