Is there any way to save edited pdf in server in pdf embed API

I've posted a functioning example on CodePen.

The functional part of the code is below. The content parameter is the PDF as a ByteArray. Convert the ByteArray into a Blob then add it to the FormData as you would any other file, then simply POST it to your server. The PHP side looks just like you uploaded a file.

To run the demo, go to the CodePen, add a comment, then Save the file. The file will get sent to my server and then zipped; this is just to make it clear that the normal save function was replaced. You'll see the UI change to a message that will let you download the zipped file. Open the zip and you should see your commented PDF.

adobeDCView.registerCallback(
    AdobeDC.View.Enum.CallbackType.SAVE_API,
    function (metaData, content, options) {
        var uint8Array = new Uint8Array(content);
        var blob = new Blob([uint8Array], { type: 'application/pdf' });
        formData = new FormData();
        var pdfFilename = urlToPDF.split("/").slice(-1)[0];
        pdfFilename = pdfFilename.split(".")[0] + "-" + uuidv4() + ".pdf";
        formData.append('pdfFile', blob, pdfFilename);

        var zipFileName = pdfFilename.replace(".pdf", ".zip");

        fetch("https://practicalpdf.com/code-pens/reflect/", {
            method: 'POST',
            body: formData,
        })
            .then(
                function (response) {
                    if (response.status == 200) {
                        updateSaveUI(zipFileName);
                    }
                }
            )

        return new Promise((resolve, reject) => {
            resolve({
                code: AdobeDC.View.Enum.ApiResponseCode.SUCCESS,
                data: {
                    metaData: { fileName: urlToPDF.split("/").slice(-1)[0] }
                }
            });
        });
    },
    saveOptions
);

Yes, that should be possible. Please refer to the public facing Embed APIs documentation for Save API here.