  The combination of magnetic symmetries and electronic band topology provides
a promising route for realizing topologically nontrivial quasiparticles, and
the manipulation of magnetic structures may enable the switching between
topological phases, with the potential for achieving functional physical
properties. Here, we report measurements of the electrical resistivity of
EuCd$_2$As$_2$ under pressure, which show an intriguing insulating dome at
pressures between $p_{\rm c1}\sim1.0$~GPa and $p_{\rm c2}\sim2.0$~GPa, situated
between two regimes with metallic transport. The insulating state can be fully
suppressed by a small magnetic field, leading to a colossal negative
magnetoresistance on the order of $10^5$\%, accessible via a modest field of
$\sim0.2$~T. First-principles calculations reveal that the dramatic evolution
of the resistivity under pressure is due to consecutive transitions of
EuCd$_2$As$_2$ from a magnetic topological insulator to a trivial insulator,
and then to a Weyl semimetal, with the latter resulting from a pressure-induced
change in the magnetic ground state. Similarly, the colossal magnetoresistance
results from a field-induced polarization of the magnetic moments, transforming
EuCd$_2$As$_2$ from a trivial insulator to a Weyl semimetal. These findings
underscore weak magnetic exchange couplings and spin anisotropy as ingredients
for discovering tunable magnetic topological materials with desirable
functionalities.
