diff --git a/DifferentiationInterface/CHANGELOG.md b/DifferentiationInterface/CHANGELOG.md
index 22d83c275..af8d11e0c 100644
--- a/DifferentiationInterface/CHANGELOG.md
+++ b/DifferentiationInterface/CHANGELOG.md
@@ -9,6 +9,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [0.7.1]
 
+### Feat
+
+- Use Mooncake's internal copy utilities ([#809])
+
 ### Fixed
 
 - Take `absstep` into account for FiniteDiff ([#812])
@@ -42,6 +46,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 [#812]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/812
 [#810]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/810
+[#809]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/809
 [#799]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/799
 [#795]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/795
 [#790]: https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/790
diff --git a/DifferentiationInterface/Project.toml b/DifferentiationInterface/Project.toml
index 5896be5b2..11be6b77d 100644
--- a/DifferentiationInterface/Project.toml
+++ b/DifferentiationInterface/Project.toml
@@ -74,7 +74,7 @@ JET = "0.9"
 JLArrays = "0.2.0"
 JuliaFormatter = "1,2"
 LinearAlgebra = "1"
-Mooncake = "0.4.88"
+Mooncake = "0.4.122"
 Pkg = "1"
 PolyesterForwardDiff = "0.1.2"
 Random = "1"
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
index 52e742b05..6253ea229 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
@@ -10,13 +10,12 @@ using Mooncake:
     tangent_type,
     value_and_gradient!!,
     value_and_pullback!!,
-    zero_tangent
+    zero_tangent,
+    _copy_output,
+    _copy_to_output!!
 
 DI.check_available(::AutoMooncake) = true
 
-copyto!!(dst::Number, src::Number) = convert(typeof(dst), src)
-copyto!!(dst, src) = DI.ismutable_array(dst) ? copyto!(dst, src) : convert(typeof(dst), src)
-
 get_config(::AutoMooncake{Nothing}) = Config()
 get_config(backend::AutoMooncake{<:Config}) = backend.config
 
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/onearg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/onearg.jl
index d637a01bd..dac2039ce 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/onearg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/onearg.jl
@@ -30,11 +30,11 @@ function DI.value_and_pullback(
 ) where {F,Y,C}
     DI.check_prep(f, prep, backend, x, ty, contexts...)
     dy = only(ty)
-    dy_righttype = dy isa tangent_type(Y) ? dy : copyto!!(prep.dy_righttype, dy)
+    dy_righttype = dy isa tangent_type(Y) ? dy : _copy_to_output!!(prep.dy_righttype, dy)
     new_y, (_, new_dx) = value_and_pullback!!(
         prep.cache, dy_righttype, f, x, map(DI.unwrap, contexts)...
     )
-    return new_y, (mycopy(new_dx),)
+    return new_y, (_copy_output(new_dx),)
 end
 
 function DI.value_and_pullback(
@@ -47,11 +47,12 @@ function DI.value_and_pullback(
 ) where {F,Y,C}
     DI.check_prep(f, prep, backend, x, ty, contexts...)
     ys_and_tx = map(ty) do dy
-        dy_righttype = dy isa tangent_type(Y) ? dy : copyto!!(prep.dy_righttype, dy)
+        dy_righttype =
+            dy isa tangent_type(Y) ? dy : _copy_to_output!!(prep.dy_righttype, dy)
         y, (_, new_dx) = value_and_pullback!!(
             prep.cache, dy_righttype, f, x, map(DI.unwrap, contexts)...
         )
-        y, mycopy(new_dx)
+        y, _copy_output(new_dx)
     end
     y = first(ys_and_tx[1])
     tx = last.(ys_and_tx)
@@ -126,7 +127,7 @@ function DI.value_and_gradient(
 ) where {F,C}
     DI.check_prep(f, prep, backend, x, contexts...)
     y, (_, new_grad) = value_and_gradient!!(prep.cache, f, x, map(DI.unwrap, contexts)...)
-    return y, mycopy(new_grad)
+    return y, _copy_output(new_grad)
 end
 
 function DI.value_and_gradient!(
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/twoarg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/twoarg.jl
index 24cb39e41..d0bbf282d 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/twoarg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/twoarg.jl
@@ -58,7 +58,7 @@ function DI.value_and_pullback(
         map(DI.unwrap, contexts)...,
     )
     copyto!(y, y_after)
-    return y, (mycopy(dx),)
+    return y, (_copy_output(dx),)
 end
 
 function DI.value_and_pullback(
@@ -83,7 +83,7 @@ function DI.value_and_pullback(
             map(DI.unwrap, contexts)...,
         )
         copyto!(y, y_after)
-        mycopy(dx)
+        _copy_output(dx)
     end
     return y, tx
 end