You cannot easily cancel Objective-C blocks that are running on a background queue. One possible solution is to let the block capture an object -- the so-called "cancel ticket" -- that determines whether it should stop or not. Whoever holds the ticket can call [ticket cancel] to stop the block. Of course, this does require the block to periodica…

ExampleViewController.m

// Shows how to use the cancel ticket to abort the async block.

#import "ExampleViewController.h"
#import "MHCancelTicket.h"

@implementation ExampleViewController
{
	MHCancelTicket *_cancelTicket;
}

- (IBAction)startAction:(id)sender
{
	if (_cancelTicket == nil)
	{
		_cancelTicket = [self startExpensiveOperation];
	}
}

- (IBAction)stopAction:(id)sender
{
	if (_cancelTicket != nil)
	{
		[_cancelTicket cancel];
		_cancelTicket = nil;
	}
}

- (MHCancelTicket *)startExpensiveOperation
{
	MHCancelTicket *ticket = [MHCancelTicket cancelTicket];

	dispatch_async(dispatch_get_global_queue(DISPATCH_QUEUE_PRIORITY_DEFAULT, 0), ^
	{
		while (!ticket.isCancelled)
		{
			// do your computations here!
		}
	});

	return ticket;
}

@end

MHCancelTicket.h

@interface MHCancelTicket : NSObject

@property (atomic, assign, readonly) BOOL isCancelled;

+ (instancetype)cancelTicket;

- (void)cancel;

@end

MHCancelTicket.m

#import "MHCancelTicket.h"

@interface MHCancelTicket ()
@property (atomic, assign, readwrite) BOOL isCancelled;
@end

@implementation MHCancelTicket

+ (instancetype)cancelTicket
{
	return [[[self class] alloc] init];
}

- (void)cancel
{
	self.isCancelled = YES;
}

@end