Large vision-language models (VLMs) have demonstrated remarkable capabilities in open-world multimodal understanding, yet their high computational overheads pose great challenges for practical deployment. Some recent works have proposed methods to accelerate VLMs by pruning redundant visual tokens guided by the attention maps of VLM's early layers. Despite the success of these token pruning methods, they still suffer from two major shortcomings: (i) considerable accuracy drop due to insensitive attention signals in early layers, and (ii) limited speedup when generating long responses (e.g., 30 tokens). To address the limitations above, we present TwigVLM -- a simple and general architecture by growing a lightweight module, named twig, upon an early layer of the base VLM. Compared with most existing VLM acceleration methods purely based on visual token pruning, our TwigVLM not only achieves better accuracy retention by employing a twig-guided token pruning (TTP) strategy, but also yields higher generation speed by utilizing a self-speculative decoding (SSD) strategy. Taking LLaVA-1.5-7B as the base VLM, experimental results show that TwigVLM preserves 96% of the original performance after pruning 88.9% of the visual tokens and achieves 154% speedup in generating long responses, delivering significantly better performance in terms of both accuracy and speed over the state-of-the-art VLM acceleration methods. Moreover, we extend TwigVLM to an improved TwigVLM++ variant by introducing a novel multi-head twig architecture with a specialized pruning head. TwigVLM++ improves pruning quality via a two-stage training paradigm combining a distillation learning stage and a pruning-oriented reinforcement learning stage, and further accelerates inference via a tree-based SSD strategy.