"the servant of the L-rd": Scripture speaks not in denigration of Moses, but in praise of him. For thus do we find with the first prophets that they were called (in praise) "servants," viz. (Amos 3:7) "For the L-rd G-d will not do anything unless He reveals His secret to His servants, the prophets."
"by the word of the L-rd.": When G-d takes the souls of the righteous, He does so gently. To what may this be compared? To a trustworthy man in a city, with whom everyone deposited their pledges. When one of them would come to claim it, he would (immediately) take it out and hand it to him, knowing exactly where it was. But when he came to send it through his son, or servant, or messenger, they would turn things topsy-turvy, not knowing their locations. Similarly, when G-d takes the souls of the righteous, He does so gently, and when He takes the souls of the wicked, He relegates (the task) to cruel, evil angels, who wrest out their souls. And thus is it written (Proverbs 13:11) "and a cruel angel will be sent against him," and (Iyyov 36:14) "Their souls will die amidst turmoil."