diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 73892da2cbf71..15adb74e27ba7 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -817,7 +817,7 @@ Groupby/resample/rolling
 - Bug in :meth:`Rolling.min` and :meth:`Rolling.max`: Growing memory usage after multiple calls when using a fixed window (:issue:`30726`)
 - Bug in :meth:`GroupBy.agg`, :meth:`GroupBy.transform`, and :meth:`GroupBy.resample` where subclasses are not preserved (:issue:`28330`)
 - Bug in :meth:`GroupBy.rolling.apply` ignores args and kwargs parameters (:issue:`33433`)
-
+- Bug in :meth:`DataFrameGroupby.std` and :meth:`DataFrameGroupby.sem` would modify grouped-by columns when ``as_index=False`` (:issue:`10355`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index d9b65f92ac0e1..b630aed69be10 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -649,11 +649,11 @@ def _set_group_selection(self):
         ):
             return
 
-        ax = self.obj._info_axis
         groupers = [g.name for g in grp.groupings if g.level is None and g.in_axis]
 
         if len(groupers):
             # GH12839 clear selected obj cache when group selection changes
+            ax = self.obj._info_axis
             self._group_selection = ax.difference(Index(groupers), sort=False).tolist()
             self._reset_cache("_selected_obj")
 
@@ -1368,8 +1368,18 @@ def std(self, ddof: int = 1):
         Series or DataFrame
             Standard deviation of values within each group.
         """
-        # TODO: implement at Cython level?
-        return np.sqrt(self.var(ddof=ddof))
+        result = self.var(ddof=ddof)
+        if result.ndim == 1:
+            result = np.sqrt(result)
+        else:
+            cols = result.columns.get_indexer_for(
+                result.columns.difference(self.exclusions).unique()
+            )
+            # TODO(GH-22046) - setting with iloc broken if labels are not unique
+            # .values to remove labels
+            result.iloc[:, cols] = np.sqrt(result.iloc[:, cols]).values
+
+        return result
 
     @Substitution(name="groupby")
     @Appender(_common_see_also)
@@ -1416,7 +1426,19 @@ def sem(self, ddof: int = 1):
         Series or DataFrame
             Standard error of the mean of values within each group.
         """
-        return self.std(ddof=ddof) / np.sqrt(self.count())
+        result = self.std(ddof=ddof)
+        if result.ndim == 1:
+            result /= np.sqrt(self.count())
+        else:
+            cols = result.columns.get_indexer_for(
+                result.columns.difference(self.exclusions).unique()
+            )
+            # TODO(GH-22046) - setting with iloc broken if labels are not unique
+            # .values to remove labels
+            result.iloc[:, cols] = (
+                result.iloc[:, cols].values / np.sqrt(self.count().iloc[:, cols]).values
+            )
+        return result
 
     @Substitution(name="groupby")
     @Appender(_common_see_also)
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 68c8b86250e06..9d7bc749d6e89 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -573,6 +573,28 @@ def test_ops_general(op, targop):
     tm.assert_frame_equal(result, expected)
 
 
+def test_ops_not_as_index(reduction_func):
+    # GH 10355
+    # Using as_index=False should not modify grouped column
+
+    if reduction_func in ("nth", "ngroup", "size",):
+        pytest.skip("Skip until behavior is determined (GH #5755)")
+
+    if reduction_func in ("corrwith", "idxmax", "idxmin", "mad", "nunique", "skew",):
+        pytest.xfail(
+            "_GroupBy._python_apply_general incorrectly modifies grouping columns"
+        )
+
+    df = DataFrame(np.random.randint(0, 5, size=(100, 2)), columns=["a", "b"])
+    expected = getattr(df.groupby("a"), reduction_func)().reset_index()
+
+    result = getattr(df.groupby("a", as_index=False), reduction_func)()
+    tm.assert_frame_equal(result, expected)
+
+    result = getattr(df.groupby("a", as_index=False)["b"], reduction_func)()
+    tm.assert_frame_equal(result, expected)
+
+
 def test_max_nan_bug():
     raw = """,Date,app,File
 -04-23,2013-04-23 00:00:00,,log080001.log