My mother is in a nursing home and has limited space in her room. How do we tell her we cannot continue to buy her new clothes?

Your profile says your mother has dementia. This means she’s lost the ability to make rational decisions. There’s no room, nor should there be, for more clothing. Ignore the requests for more. Consider removing a good amount of what’s there and swapping it out at other times. It may seem new to her and will decrease the possibility of clothing disappearing as can happen in managed care settings. Not accusing anyone of stealing, it’s just a fact that things get lost, to the wrong room, etc. This isn’t you being mean, it’s you looking out for her at the time she cannot logically do so for herself, no explaining or discussing needed

It isn't mean to gently say:
"Mom, you have limited space, and don't need more clothes, so we aren't going to buy more for you unless there is an outfit you wish us to put in a donation bin somewhere. Love you, but you cannot clutter the room with these things".
Sweet smile. Move on.
If this is a bit of a compulsion, then you are dealing with a bit of a compulsion.
But in any case, there's nothing mean here at all.

You just say, "Ok I'll bring them next visit" and then discretely remove some, and do what Daughterof1930 suggested and bring them as the new ones.

It is not mean to say No to a person with dementia. Her brain is broken the ability to rationalize is forever gone.

You will now have to accept the responsibility to make her decisions for her.

Funky and Geaton have good ideas.

Really, you should never have brought in a rack. My Mom had nine outfits. More than enough for the laundry turn around. I put tops with matching pants. Later even her bra, long story. I only had her seasonal clothing there. Her others were in a tote in my spare bedroom.

I rotate clothes by telling my mom I am taking them home to special wash them ..she then forgets.. she thinks clothes brought back are new again!

Your mother is 97 with dementia. Do you really think she's going to know if you remove 75% of her clothing from the room, bring them home to "wash", and return some of them as new outfits???? And while you're at it, remove the clothing rack too which has no place in a cramped room and presents more of a tripping hazard than anything else!

Realize your mother is stuck in a loop thinking pattern which goes with dementia, saying she needs more clothing when she obviously does not. It's not "mean" to use techniques to distract her from thinking she needs new clothing all the time. It's helping her to have room to breathe in a tight space!

bfmtexas1: Remove the clothes rack. An elder in an NH does not require new clothing.

I would rotate some of the clothes and take the rest home to "wash" as lealonnie suggests since she will not remember which ones you took home. I would keep the nicest and newest ones in the drawers and rotate some in the closest.

Tell her that you will help her to "freshen up" her wardrobe seasonally. Then, go through her clothes to weed out ones not suitable for the weather - for storage. Let her look through magazines for the "current fashion" and encourage her to make a wish list. Buy only a few items to "freshen up" her wardrobe: think scarf, a new top, an accessory....