diff --git a/mlir/include/mlir/IR/Operation.h b/mlir/include/mlir/IR/Operation.h
--- a/mlir/include/mlir/IR/Operation.h
+++ b/mlir/include/mlir/IR/Operation.h
@@ -85,7 +85,10 @@
   /// original one, but they will be left empty.
   /// Operands are remapped using `mapper` (if present), and `mapper` is updated
   /// to contain the results.
-  Operation *cloneWithoutRegions(BlockAndValueMapping &mapper);
+  /// The `mapResults` argument specifies whether the results of the operation
+  /// should also be mapped.
+  Operation *cloneWithoutRegions(BlockAndValueMapping &mapper,
+                                 bool mapResults = true);
 
   /// Create a partial copy of this operation without traversing into attached
   /// regions. The new operation will have the same number of regions as the
diff --git a/mlir/lib/IR/Operation.cpp b/mlir/lib/IR/Operation.cpp
--- a/mlir/lib/IR/Operation.cpp
+++ b/mlir/lib/IR/Operation.cpp
@@ -526,7 +526,8 @@
 /// Create a deep copy of this operation but keep the operation regions empty.
 /// Operands are remapped using `mapper` (if present), and `mapper` is updated
 /// to contain the results.
-Operation *Operation::cloneWithoutRegions(BlockAndValueMapping &mapper) {
+Operation *Operation::cloneWithoutRegions(BlockAndValueMapping &mapper,
+                                          bool mapResults) {
   SmallVector<Value, 8> operands;
   SmallVector<Block *, 2> successors;
 
@@ -545,8 +546,10 @@
                        successors, getNumRegions());
 
   // Remember the mapping of any results.
-  for (unsigned i = 0, e = getNumResults(); i != e; ++i)
-    mapper.map(getResult(i), newOp->getResult(i));
+  if (mapResults) {
+    for (unsigned i = 0, e = getNumResults(); i != e; ++i)
+      mapper.map(getResult(i), newOp->getResult(i));
+  }
 
   return newOp;
 }
@@ -562,12 +565,15 @@
 /// sub-operations to the corresponding operation that is copied, and adds
 /// those mappings to the map.
 Operation *Operation::clone(BlockAndValueMapping &mapper) {
-  auto *newOp = cloneWithoutRegions(mapper);
+  auto *newOp = cloneWithoutRegions(mapper, /*mapResults=*/false);
 
   // Clone the regions.
   for (unsigned i = 0; i != numRegions; ++i)
     getRegion(i).cloneInto(&newOp->getRegion(i), mapper);
 
+  for (unsigned i = 0, e = getNumResults(); i != e; ++i)
+    mapper.map(getResult(i), newOp->getResult(i));
+
   return newOp;
 }