diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
@@ -928,11 +928,15 @@ def _break_share_link(ax, grouper):
         self.stale = True
         self._localaxes.remove(ax)
 
+        # Break link between any shared axes
         for name in ax._axis_names:
             last_ax = _break_share_link(ax, ax._shared_axes[name])
             if last_ax is not None:
                 _reset_locators_and_formatters(getattr(last_ax, f"{name}axis"))
 
+        # Break link between any twinned axes
+        _break_share_link(ax, ax._twinned_axes)
+
     # Note: in the docstring below, the newlines in the examples after the
     # calls to legend() allow replacing it with figlegend() to generate the
     # docstring of pyplot.figlegend.

diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -4663,6 +4663,21 @@ def test_spectrum():
             ax.set(xlabel="", ylabel="")
 
 
+@check_figures_equal(extensions=['png'])
+def test_twin_remove(fig_test, fig_ref):
+    ax_test = fig_test.add_subplot()
+    ax_twinx = ax_test.twinx()
+    ax_twiny = ax_test.twiny()
+    ax_twinx.remove()
+    ax_twiny.remove()
+
+    ax_ref = fig_ref.add_subplot()
+    # Ideally we also undo tick changes when calling ``remove()``, but for now
+    # manually set the ticks of the reference image to match the test image
+    ax_ref.xaxis.tick_bottom()
+    ax_ref.yaxis.tick_left()
+
+
 @image_comparison(['twin_spines.png'], remove_text=True)
 def test_twin_spines():