Drain pipe through floor joist
It depends on the size of your drain.  You can do it with a 1.5&quot; PVC but a 2&quot; really won't work.
Allowable hole size in joist
The maximum allowed hole you can drill in a joist is 1/3rd the depth of that joist.  The actual depth of a 2x8 joist is 7.25&quot; allowing only a 2.4&quot; hole.
A 2&quot; PVC pipe is 2.375&quot; outer diameter (2-3/8&quot;) and you'll probably never get a 2.375&quot; pipe into a 2.4&quot; hole.  Milwaukee is the brand plumbers use in my area and Milwaukee's hole saw kits don't even come with 2-3/8&quot; saws because they're not practical.
If your drain is 1.5&quot;, Family Handyman has a helpful article showing you the right way to plan where to drill the hole in your joist.  Note you need to plan on a 1/4&quot; slope per foot of drain line, too; so don't figure on going through very many joists in series with this drain, or you'll be too far from the center of the joists and compromise them.
1.5&quot; drain capacity
A 1.5&quot; drain is only enough for 3 drainage fixture units (DFUs).  That's sufficient for your kitchen sink &amp; garbage disposal (DFUs per fixture table) but it is not enough for an additional dishwasher to meet code.