diff --git a/pkg/planner/core/logical_plan_builder.go b/pkg/planner/core/logical_plan_builder.go
index 09d54b68e7..03e2384241 100644
--- a/pkg/planner/core/logical_plan_builder.go
+++ b/pkg/planner/core/logical_plan_builder.go
@@ -15,6 +15,7 @@
 package core
 
 import (
+	"cmp"
 	"context"
 	"fmt"
 	"maps"
@@ -5269,6 +5270,11 @@ func (t *TblColPosInfo) MemoryUsage() (sum int64) {
 	return
 }
 
+// Cmp compares two TblColPosInfo by their Start field.
+func (t *TblColPosInfo) Cmp(a TblColPosInfo) int {
+	return cmp.Compare(t.Start, a.Start)
+}
+
 // TblColPosInfoSlice attaches the methods of sort.Interface to []TblColPosInfos sorting in increasing order.
 type TblColPosInfoSlice []TblColPosInfo
 
@@ -5277,16 +5283,6 @@ func (c TblColPosInfoSlice) Len() int {
 	return len(c)
 }
 
-// Swap implements sort.Interface#Swap.
-func (c TblColPosInfoSlice) Swap(i, j int) {
-	c[i], c[j] = c[j], c[i]
-}
-
-// Less implements sort.Interface#Less.
-func (c TblColPosInfoSlice) Less(i, j int) bool {
-	return c[i].Start < c[j].Start
-}
-
 // FindTblIdx finds the ordinal of the corresponding access column.
 func (c TblColPosInfoSlice) FindTblIdx(colOrdinal int) (int, bool) {
 	if len(c) == 0 {
@@ -5321,7 +5317,9 @@ func buildColumns2HandleWithWrtiableColumns(
 			cols2Handles = append(cols2Handles, TblColPosInfo{TblID: tblID, Start: offset, End: end, HandleCols: handleCol})
 		}
 	}
-	sort.Sort(cols2Handles)
+	slices.SortFunc(cols2Handles, func(a, b TblColPosInfo) int {
+		return a.Cmp(b)
+	})
 	return cols2Handles, nil
 }
 
@@ -5363,8 +5361,9 @@ func pruneAndBuildColPositionInfoForDelete(
 		}
 	}
 	// Sort by start position. To do the later column pruning.
-	// TODO: `sort`` package has a rather worse performance. We should replace it with the new `slice` package.
-	sort.Sort(cols2PosInfos)
+	slices.SortFunc(cols2PosInfos, func(a, b TblColPosInfo) int {
+		return a.Cmp(b)
+	})
 	prunedColCnt := 0
 	var err error
 	for i := range cols2PosInfos {
diff --git a/pkg/planner/core/rule_partition_processor.go b/pkg/planner/core/rule_partition_processor.go
index cc36282f33..8e9f5f3c8e 100644
--- a/pkg/planner/core/rule_partition_processor.go
+++ b/pkg/planner/core/rule_partition_processor.go
@@ -931,6 +931,10 @@ type partitionRange struct {
 	end   int
 }
 
+func (p *partitionRange) Cmp(a partitionRange) int {
+	return cmp.Compare(p.start, a.start)
+}
+
 // partitionRangeOR represents OR(range1, range2, ...)
 type partitionRangeOR []partitionRange
 
@@ -958,14 +962,6 @@ func (or partitionRangeOR) Len() int {
 	return len(or)
 }
 
-func (or partitionRangeOR) Less(i, j int) bool {
-	return or[i].start < or[j].start
-}
-
-func (or partitionRangeOR) Swap(i, j int) {
-	or[i], or[j] = or[j], or[i]
-}
-
 func (or partitionRangeOR) union(x partitionRangeOR) partitionRangeOR {
 	or = append(or, x...)
 	return or.simplify()
@@ -977,13 +973,14 @@ func (or partitionRangeOR) simplify() partitionRangeOR {
 		return or
 	}
 	// Make the ranges order by start.
-	sort.Sort(or)
-	sorted := or
+	slices.SortFunc(or, func(i, j partitionRange) int {
+		return i.Cmp(j)
+	})
 
 	// Iterate the sorted ranges, merge the adjacent two when their range overlap.
 	// For example, [0, 1), [2, 7), [3, 5), ... => [0, 1), [2, 7) ...
-	res := sorted[:1]
-	for _, curr := range sorted[1:] {
+	res := or[:1]
+	for _, curr := range or[1:] {
 		last := &res[len(res)-1]
 		if curr.start > last.end {
 			res = append(res, curr)