While the existing literature on collaborative writing has implied the benefits of its implementation in second language (L2) classrooms for students' language learning, the assessment of collaborative writing has received scant attention in both language assessment literature and L2 writing literature. This study proposes an assessment scheme considering both products and processes when assessing online writing undertaken collaboratively. It employs a case study approach to explore two pairs of Chinese students' motivation toward assessed collaborative writing tasks. Drawing on data from participants' reflections, pair interviews, stimulated recall interviews, online pair-talks, and revision histories, this study reveals that students with similar L2 proficiency may hold different motivations during product-graded, web-based collaborative writing assignments compared to product & process-graded assignments of the same nature. Additionally, this study finds that assessment can lead to changes in students' motivations, which in turn affect learner participation in collaborative writing. The results can enhance our comprehension of the impact of assessment on learners' motivation in computer-mediated collaborative writing tasks, offering fresh insights into strategies for strengthening learner motivation during the implementation of such tasks. The study suggests teachers should prioritize assessment as a pivotal element when incorporating computer-assisted collaborative writing, conscientiously consider students' motivations in activity design, and recognize the growing significance of computer technologies in L2 learning.