Deep learning (DL) based semantic communication methods have been explored for the efficient transmission of images, text, and speech in recent years. In contrast to traditional wireless communication methods that focus on the transmission of abstract symbols, semantic communication approaches attempt to achieve better transmission efficiency by only sending the semantic-related information of the source data. In this paper, we consider semantic-oriented speech transmission which transmits only the semanticrelevant information over the channel for the speech recognition task, and a compact additional set of semantic-irrelevant information for the speech reconstruction task. We propose a novel end-to-end DLbased transceiver which extracts and encodes the semantic information from the input speech spectrums at the transmitter and outputs the corresponding transcriptions from the decoded semantic information at the receiver. In particular, we employ a soft alignment module and a redundancy removal module to extract only the text-related semantic features while dropping semantically redundant content, greatly reducing the amount of semantic redundancy compared to existing methods. We also propose a semantic correction module to further correct the predicted transcription with semantic knowledge by leveraging a pretrained language model. For the speech to speech transmission, we further include a CTC alignment module that extracts a small number of additional semantic-irrelevant but speech-related information, such as duration, pitch, power and speaker identification of the speech for the better reconstruction of the original speech signals at the receiver. We also introduce a two-stage training scheme which speeds up the training of the proposed DL model. The simulation results confirm that our proposed