Alignment-based quality attributes have identified several variants of SARS-CoV-2(severe acute respiratory syndrome coronavirus 2) that causes COVID-19 pandemic, but they face challenges to provide dynamic trajectory and origin of these variants. This study employs an alignment-free approach combining Fréchet distance (Fr) and artificial recurrent neural network to reveal evolutionary trajectory and origin of SARS-CoV-2 variant. Fr generates a distance matrix of 84 genome features and more than one million of genome sequences. Recurrent neural networks use this Fr matrix to quantitatively identify variants and reveal the evolutionary trajectory and origin of SARS-CoV-2. Total 34 SARS-CoV-2 variants have been identified. All these variants dynamically delete their genome during evolution, but their trajectory and deletion degree varies with individual variants, which can be classified into 3 groups, slight mutation group (13 members), middle level deletion (17 members), and high deletion (4 members). The slight deletion group works like wild type and its trajectory waves only slightly and temporarily, which has very low infection capacity. The high deletion group fluctuates with a rough trajectory characterized as a large loss and it also infects humans lightly. The middle deletion group gradually deletes their genome with a certain rhythm trajectory, corresponding to the pandemic peaks. This group causes most of the global COVID-19 cases. At least 3 mink coronavirus variants pose 56 genome features similar to SARS-CoV-2 and they are predicted to be able to infect human, and thus mink is the most likely origin of SARS-CoV-2, and the origin path follows this order: mink, cat, tiger, mouse, hamster, dog, lion, gorilla, leopard, bat, and pangolin. Therefore, this mink-origin SARS-CoV-2 evolves with a gradual deletion rhythm to infect humans