That picture shows a Mesh with 9 Rows of Holes. And 10 Rows of Metal between the Hole Rows.
If you remove 1 Row of Metal, then it would be Interesting to see if the Resistance Increased 1/10th of the Resistance of the Mesh before you cut anything?
Resistance is inversely related to the cross sectional area of the wire. If you reduce the cross section by half, the resistance doubles. If you start with 10 wires in your mesh strip, measure the resistance of it, you can do the math to get to the number of wires you want.
In zoidman's example, removing one wire would increase the resistance by a factor of 10/9 or 1.11 or 11%.
Removing 5 wires would increase the resistance by a factor of 10/5 or 2.0 and double the resistance.
zoidman, your instincts were right. Punching holes in it would surely cause hot spots.
Round wire isn't as easy. Doubling the diameter reduces the resistance by a factor of four.