If I negate a monster's effect with XYZ Block and send an XYZ Material to the GY and the opponent activates Karma Cut after and targets and banishes the XYZ monster, does XYZ Block still activate?
Yes, you opponent can't activate karma in response to xyz block since it is a counter trap. You detach 1 material -> the effect is negated -> card is destroyed -> end of the chain. After this your opp can activate karma but it'd be too late