It would depend on your printer model. Check your printer user manual to see if it has a borderless printing option. Not all printers have this functionality.
There are some consumer inkjet printers that can do this. I have a Canon inkjet printer which can do it, and there is no gripper edge issue either - bleed on all four edges is possible. There is a borderless printing option which can be selected in the print properties. Results are generally good, and I've never really had a problem using it. The printer itself has a method of collecting the ink that's sprayed over the edge of the sheet - so there is no build up of ink inside the machine.
To use it (in the example below I'm using LibreOffice Calc, because I don't use MS Excel), you need to click on the "Properties" button in the main print dialog, and this opens up the full print properties. With my particular printer it works best on glossy photo paper, and is "not recommended" for regular uncoated paper - so this might be an issue for you.
Note however that you will lose a little of the image as there has to be a slight overlap, so it might not be entirely practical for your particular usage.
By the way, this is not a recommendation for a particular print model or manufacturer. I have no links with Canon, although I have used their printers for many years, in particular for large format printing (not the model shown).