There are several ways to make a switched current mirror,
which one you'd choose depends on accuracy and settling
time required, mostly.
You could have a simple current mirror and jerk its gate
rail between active and shunted. This will have a large
swing driven by a low current, neither spectacularly
accurate nor fast.
You could have a cascode mirror and inject a current
into the mid-point that exceeds the set-current, which
is basically source-steering; that node is low impedance
and the signal swing can be small, if controlled well.
You could use a simple diff pair attached to the present
source (or sink), and this can be steered by a few
hundred mV swing.