In just four short lines, a speaker sits in front of a doctor and offers up his own body. The odd phrase "saving time" gives the moment a dry, almost ironic edge. Time is what a dying person has least of, yet here it becomes something to economize, and the speaker seems to hand over himself quickly, without ceremony.
The most striking move is how he describes himself: "this strange man dying so." He speaks as if he were a stranger, someone to be examined from outside. That distance suggests a mind trying to cope by stepping back from its own mortality. Yet the final line, "this open self," pulls the other way. Being open can mean exposed on an examining table, but it also suggests honesty and surrender.
The mood is quiet, restrained, and quietly raw. There is no loud grief, only a calm, vulnerable offering, which fits the title. The poem leaves us with a sense of trust mixed with fear.