This is because you've cut into a point where there's an audio signal present.
You could try cutting at a zero crossing point - ymmv with this though, it's not 100% foolproof
Instead of cutting a part out, you could try simply setting appropriate punch points and punch in
You could also try recording the flubbed bit onto a new track and use track automation to fade the old data out & back in using tightly defined curves
You could use a 3rd party wave editor to home in on the clicks and edit them out
You could use clip automation on what you've already recorded - again using nearly vertical - but not quite vertical! fades