Can my mother legally sign papers with a score of 21 out of 30 on MMSE test by her family doctor?

As PP mentioned, a notary or lawyer may ask her questions to determine if she understands what she is signing.   We had to cancel once till the notary could come to the house on a "good" day of moms. 

Another risk is if there are disputes among family members, one may assert that mom did not know what she was signing, and may challenge in court.

You need a Durable Power of Attorney (DPOA) and a Healthcare Directive and Power of Attorney (HCPOA) signed while your mother is still considered legally competent. Yes, she may still be considered legally competent while scoring 21. Often people in the early stages of a cognitive decline are still legally competent for some time. For example, Mom may be having problems paying her bills on time _but_ she still knows what her bills are and wants her bills to be paid so Mom is competent to direct her POA pay her bills. I suggest getting a letter from her doctor stating she is competent and then contacting an attorney ASAP.

If this is involving a lawyer or notary I think that you need to be be upfront in discussing her mild impairment with them beforehand, and then allowing them time with your mother to ascertain whether she comprehends what she is asking for.

21/30 on the MMSE is classified as "Mild Impairment". What sort of papers does mom need to sign?