The speaker is a miser, and the poem lets him explain, with dry pride, how he saves money. He doesn't own a clock. His stomach tells him when it's time to eat, and he finds that handy. The oddest line is the one that calls a clock "a gun for heirs." The idea seems to be that a clock counts down a life, and the people waiting to inherit are the ones who benefit when time runs out. Judging by the wording, they "make the best of a bad market," as if death were a sale.
By refusing the clock, the speaker refuses to play along. He keeps his own time and his own money. The last two lines show how that plays out: he parts "very kindly" from others, politely turning down invitations, and "dines at home." The tone is deadpan and a little funny, but it is also lonely. His thrift protects him from heirs and hosts, and it also keeps him by himself.