The spoken language serves as an accessible and efficient interface, enabling non-experts and disabled users to interact with complex assistant robots. However, accurately grounding language utterances gives a significant challenge due to the acoustic variability in speakers' voices and environmental noise. In this work, we propose a novel speech-scene graph grounding network (SGGNet$^2$) that robustly grounds spoken utterances by leveraging the acoustic similarity between correctly recognized and misrecognized words obtained from automatic speech recognition (ASR) systems. To incorporate the acoustic similarity, we extend our previous grounding model, the scene-graph-based grounding network (SGGNet), with the ASR model from NVIDIA NeMo. We accomplish this by feeding the latent vector of speech pronunciations into the BERT-based grounding network within SGGNet. We evaluate the effectiveness of using latent vectors of speech commands in grounding through qualitative and quantitative studies. We also demonstrate the capability of SGGNet$^2$ in a speech-based navigation task using a real quadruped robot, RBQ-3, from Rainbow Robotics.