Controlling chatbot utterance generation with multiple attributes such as personalities, emotions and dialogue acts is a practically useful but under-studied problem. We propose a novel controllable generation framework called DASC that possesses strong controllability with weighted decoding paradigm, while improving generation quality with the grounding in an attribute semantics space. Generation with multiple attributes is then intuitively implemented with an interpolation of multiple attribute embeddings. Experiments show that DASC can achieve state-of-the-art control accuracy in 3-aspect controllable generation tasks while also producing interesting and reasonably sensible responses, even if in an out-of-distribution robustness test. Visualization of the meaningful representations learned in the attribute semantic space also supports its effectiveness.