Mixup generates augmented samples by linearly interpolating inputs and labels with a controllable ratio. However, since it operates at the latent embedding level, the resulting samples are not human-interpretable. In contrast, LLM-based augmentation methods produce sentences via prompts at the token level, yielding readable outputs but offering limited control over the generation process. Inspired by recent advances in LLM inversion, which reconstructs natural language from embeddings and helps bridge the gap between latent embedding space and discrete token space, we propose inversedMixup, a unified framework that combines the controllability of Mixup with the interpretability of LLM-based generation. Specifically, inversedMixup aligns the output embedding space of a task-specific model with the input embedding space of an LLM, so that mixed embeddings can be reconstructed, under a controllable mixing ratio, into human-interpretable sentences. This interpretability provides the first empirical evidence of the manifold intrusion phenomenon in text Mixup. Building on this, we extend inversedMixup into a three-stage data augmentation method, and introduce a simple yet effective strategy to mitigate manifold intrusion during augmentation. Extensive experiments demonstrate the effectiveness and generalizability of our approach in both few-shot and fully supervised scenarios.