These stems are in drinking water for 3~4 days. The edges of leaves show blackening and drying. What is the reason behind it and how do I avoid it?

Starting cuttings in water is problematic because if they actually grow roots, the roots are damaged or destroyed when you plant in soil.

But if you really want to, 2 or 3 leafless nodes need to be under water and the water must be changed daily. There is no oxygen in dirty water, so no roots will grow.

Try it in soil. Take a cutting, cut the leaves off the bottom 3 nodes and bury the stems in a pot of soil. Keep it watered.

The black leaf may be bruise, or too cold the water you use, mints like warmth on their feet, for rooting, also don't keep them in strong light, the roots need dark to grow.