Anything that is already brown is dead so cutting it off will not stress the plant any further. You don't say where you live and if this is inside or outside but if it is inside take it outside immediately. Roses are not houseplants, They nearly ALWAYS get spider mites inside. I would soak the entire plant, canes and all, in a bucket of water for an hour or so to kill off the spider mites and their eggs. If it's still in it's original small pot it probably needs a bigger pot and fresh potting soil too.

Yes, cut off any canes that are all brown. Any that have green bottoms cut to the healthy green. This can only help. Provide shade for the rose until it can recover. No fertilizers until she's healthy again. Try to keep the rose moist but not wet. If your able spray with fine mist spray bottle the bottoms of leaves with water only so mites don't start up again. I mentioned fine mist only because you don't want the soil to get too wet. That depends on what size pot the rose is in. Hope she recovers for you.

Thanks a lot Patty and Seil for your helpful comments. I am new to this and have no idea, so your comments are very useful.

I am living in the UK and yes the plant stays inside since I did not want to expose it to the cloudy and cold (10 degree C) weather outside. I did give some NPK type fertiliser granules before which are still on the soil, so you suggest removing these granules?

It is still in the original small pot and currently has no leaves as it was heavily infested with mites and leaves wilted. As I mentioned some branches are still green but others entirely brown or brown almost till the union. I will cut-off the brown ones immediately.

Do you suggest keeping it outside now or in a shady place inside so that it can recover away from direct sunlight?

Thanks a lot again for your helpful comments. I do really appreciate this.

Outside in bright shade until she shows signs of new growth would be best. Seils advice on larger pot is correct. I'm not sure if now is good or not for a stressed plant. I would probably wait for better health, Seil would know better on this than I do. Is 10 c your daytime high today or night time low.

Thanks Patty!

Looking at the current weather, the day time high is 19 degree C and night time low is 11 degree C. The plant was always inside and as you know in the UK it often drizzles, so do you recommend keep it outside even if the weather is not all bright and sunny?

At the moment all the buds looks very dried and severely dehydrated after the eucalyptus oil application but the green part of the surviving cane still looks healthy. It is now basically a few dried canes and few partially green but healthy looking canes without any leaves.

Your welcome and thats cold. I have to say that Seil has a lot of experience with pots and I haven't. I'm sure she will be back to help. I do want to wish you the best of luck with your rose.

If you can transplant into a little bit bigger pot without disturbing the existing root ball it shouldn't add to the stress on the plant. You don't want to go from a very small pot to a big pot all at once. You need to do it in stages, one pot size up at a time.

I converted your Celsius and you're talking about a range of 51 to 66 Fahrenheit. That is not too cold at all for roses. Roses can take temps down to about -2C before suffering any damage. At 11 to 19C they should still be growing, slowly but growing. Put it outside, in dappled shade, and give it a chance to recover. Once it leafs out again gradually move it out into full sunlight. Roses need a lot of sunlight to bloom.

Roses also like a lot of water. As long as the pot has good drainage holes so any excess water can drain out of the pot freely don't worry about the drizzle. Do not put any kind of tray under the pot that will hold water in the roots. Roses hate to sit in water and have soggy, wet roots.

Don't worry about the fertilizer that's already in the soil. Just do not add any kind of new fertilizer to the rose until it leafs back out and is growing again. Keeping it outside where it will get rained on should help flush that existing fertilizer through the soil quicker anyway.

Thanks Seil for your very detailed advice! I cut the brown and black stems and basically this means more or less everything is gone except 3 stems which are green but without leaves. I noticed some white fungus near the union in one of them and I guess that might be due to excess watering, although the water drains off quickly. I removed the fungus along with some nearby soil.

As all of you recommended, the plant is not sitting outside. Do you think it has some chances of surviving and the canes or new ones might grow? While removing some soil to get rid of the fungus, I noticed the roots are still healthy and strong.

Thanks again for all your helpful advice, really very kind of you.

Update on the rose plant: two of the four plants started to sprout and there are around 60-70 leaves now. Looks it is slowly but steadily recovering. It sits outside and looks happy!

I cannot thank you enough Seil, Patty and Jacqueline. You have just saved my plant!

Don't think I did that much to help but I sure am happy for you that it's coming back.