I know Parvati Devi killed Demon Mahishasura with help of other Shaktis by manifesting into Goddess Durga. So, Adishakti killed Mahishasura through Parvathi Devi. I think same is the case with Goddess Kaali. But on the contrary, did Lakshmi Devi or Saraswati Devi kill any demons without manifesting into Adi Shakti or Goddess Durga?
Mahishasura according to Devi-Mahatmya(Chapter 2 to 5) was killed by Mahalaksmi.The Rishi of this Madhyama-Charitra of Devi-Mahatmya (Sri Sri Chandi) is Sri Vishnu Himself, and Devata is Mahalaksmi. She appeared from the collected aura (Tejas) of Brahma-Vishnu-Shiva and the devas, who were very very angry because of the oppression by Mahishasura.(chapter 2, mantras 9-13).But She of course is one form of Adi Shakti. Also, Kamala,a form of Lakshmi, is one of the Ten Mahavidyas and Her Bhairava is Sri Vishnu.So Devi Lakshmi is also Para Shakti Herself!
There are various forms of Mahalakshmi mentioned in Sri Sri Chandi. One of such forms is worshipped as the Kolhapur (also known as Karavir) Mahalakshmi temple, which is considered one of the 51 Shakti-peethas.(An original image is enclosed which shows Her form as Mahalakshmi with his vahana Lion clearly visible as per the Dhyana-Mantra mentioned in Sri Sri Chandi)The description of Mahalakshmi according to the Pradhaanika-Rahasya of Sri Sri Devimahatmya is
srvasyadyaa mahalakshmi strigunaa parameswari/..matulingam gadaam khetam paanapaatram cha vibrati/ nagam lingam cha yonim cha bibhtati nripa murdhani// meaning She holds matulinga(a fruit), gada, khetaka,panapatra and on Her head there are naga, linga and yoni. This form is seen at Kolhapur.
Parvati in Her own form did NOT kill any demon.
I have added an image of the starting of the second character (Mahishasurasainyavadhah) from Sri Sri Chandi by Udbodhan page 81 that mentions "Om asya srimadhyamacharitrasya vishnur rishih malakshmi devata usnik chhandah saakamvari shaktih durga bijam vayus tattvam yajurvedah svarupam MAHALAKSHMI-PRITI-ARTHAM madhyamacharitra-jape viniyogah" and then describes one dhyana-mantra of Mahalakshmi.
Further page 82 gives the original and meaning of slokas from LAKSHMI-TANTRA that mentions that
Devi Lakshmi told Indra: I am Mahalakshmi myself.In sayambhuva manvantara, I again appeared for killing Mahisasura and benefiting all devas.
Goddess Mahasarasvati killed Shumbha and Nishumbha according to Sri Sri Chandi.
Durga Devi is said to killed the demon Durgama.