diff --git a/pytorch_lightning/accelerators/accelerator.py b/pytorch_lightning/accelerators/accelerator.py
index 1dcd541ca0610..f4c068f298e89 100644
--- a/pytorch_lightning/accelerators/accelerator.py
+++ b/pytorch_lightning/accelerators/accelerator.py
@@ -466,3 +466,6 @@ def connect_precision_plugin(self, plugin: PrecisionPlugin) -> None:
             ' It will be removed in v1.5.'
         )
         self.setup_precision_plugin(plugin)
+
+    def save_checkpoint(self, checkpoint: Dict[str, Any], filepath) -> None:
+        self.training_type_plugin.save_checkpoint(checkpoint, filepath)
diff --git a/pytorch_lightning/plugins/training_type/tpu_spawn.py b/pytorch_lightning/plugins/training_type/tpu_spawn.py
index a8706d54cb5c9..aee2b8914b579 100644
--- a/pytorch_lightning/plugins/training_type/tpu_spawn.py
+++ b/pytorch_lightning/plugins/training_type/tpu_spawn.py
@@ -106,8 +106,6 @@ def new_process(self, process_idx: int, trainer, mp_queue) -> None:
         trainer.accelerator.setup_optimizers(trainer)
         trainer.precision_plugin.connect(self._model, None, None)
 
-        # replace trainer save_checkpoint to use `xm.save`
-        trainer.save_checkpoint = self.save_checkpoint
         self.barrier("pre-run-stage")
 
         results = trainer.run_stage()
@@ -298,14 +296,13 @@ def test_step(self, *args, **kwargs):
     def predict_step(self, *args, **kwargs):
         return self.lightning_module.predict_step(*args, **kwargs)
 
-    def save_checkpoint(self, filepath, weights_only: bool = False):
+    def save_checkpoint(self, checkpoint: Dict[str, Any], filepath: str) -> None:
         """Save model/training states as a checkpoint file through state-dump and file-write.
 
         Args:
+            trainer: PyTorch Lightning Trainer
             filepath: write-target file's path
             weights_only: saving model weights only
         """
-        # dump states as a checkpoint dictionary object
-        _checkpoint = self.lightning_module.trainer.checkpoint_connector.dump_checkpoint(weights_only)
         # Todo: TypeError: 'mappingproxy' object does not support item assignment
-        self.save({k: v for k, v in _checkpoint.items() if k != "callbacks"}, filepath)
+        self.save({k: v for k, v in checkpoint.items() if k != "callbacks"}, filepath)
diff --git a/pytorch_lightning/plugins/training_type/training_type_plugin.py b/pytorch_lightning/plugins/training_type/training_type_plugin.py
index 08dca63a7c925..ca097c32513c6 100644
--- a/pytorch_lightning/plugins/training_type/training_type_plugin.py
+++ b/pytorch_lightning/plugins/training_type/training_type_plugin.py
@@ -22,6 +22,8 @@
 from pytorch_lightning.core.lightning import LightningModule
 from pytorch_lightning.overrides.base import unwrap_lightning_module
 from pytorch_lightning.plugins.base_plugin import Plugin
+from pytorch_lightning.utilities import rank_zero_warn
+from pytorch_lightning.utilities.cloud_io import atomic_save
 
 if TYPE_CHECKING:
     from pytorch_lightning.trainer.trainer import Trainer
@@ -192,3 +194,19 @@ def setup_optimizers_in_pre_dispatch(self) -> bool:
         Returns: If True, delay setup optimizers till pre_dispatch, else call within setup.
         """
         return False
+
+    def save_checkpoint(self, checkpoint: Dict[str, Any], filepath: str) -> None:
+        # dump states as a checkpoint dictionary object
+        if self.is_global_zero:
+            checkpoint = self.on_save(checkpoint)
+            try:
+                # write the checkpoint dictionary on the file
+                atomic_save(checkpoint, filepath)
+            except AttributeError as err:
+                if LightningModule.CHECKPOINT_HYPER_PARAMS_KEY in checkpoint:
+                    del checkpoint[LightningModule.CHECKPOINT_HYPER_PARAMS_KEY]
+                rank_zero_warn(
+                    'Warning, `hyper_parameters` dropped from checkpoint.'
+                    f' An attribute is not picklable {err}'
+                )
+                atomic_save(checkpoint, filepath)
diff --git a/pytorch_lightning/trainer/connectors/checkpoint_connector.py b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
index 60c76b70bba50..8b602fa6caa69 100644
--- a/pytorch_lightning/trainer/connectors/checkpoint_connector.py
+++ b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
@@ -386,27 +386,12 @@ def get_max_ckpt_path_from_folder(self, folder_path: Union[str, Path]) -> str:
         ckpt_number = max_suffix if max_suffix is not None else 0
         return f'{folder_path}/hpc_ckpt_{ckpt_number}.ckpt'
 
-    def save_checkpoint(self, filepath, weights_only: bool = False):
+    def save_checkpoint(self, filepath, weights_only: bool = False) -> None:
         """Save model/training states as a checkpoint file through state-dump and file-write.
 
         Args:
             filepath: write-target file's path
             weights_only: saving model weights only
         """
-        # dump states as a checkpoint dictionary object
-        checkpoint = self.dump_checkpoint(weights_only)
-        if self.trainer.is_global_zero:
-            # write the checkpoint dictionary on the file
-
-            if self.trainer.training_type_plugin:
-                checkpoint = self.trainer.training_type_plugin.on_save(checkpoint)
-            try:
-                atomic_save(checkpoint, filepath)
-            except AttributeError as err:
-                if LightningModule.CHECKPOINT_HYPER_PARAMS_KEY in checkpoint:
-                    del checkpoint[LightningModule.CHECKPOINT_HYPER_PARAMS_KEY]
-                rank_zero_warn(
-                    'Warning, `hyper_parameters` dropped from checkpoint.'
-                    f' An attribute is not picklable {err}'
-                )
-                atomic_save(checkpoint, filepath)
+        _checkpoint = self.dump_checkpoint(weights_only)
+        self.trainer.accelerator.save_checkpoint(_checkpoint, filepath)