Just to clarify before I continue this answer: I'm ignoring the mammal/reptile requirement in favour of the 'blood isn't necessary' requirement, as any creature that has no heart isn't going to easily fit into our normal tree of life. It might possibly be a shrub somewhere. Or a mushroom.
With that said: One potential (though unlikely) solution might be the generation of 'self aware' emergent intelligence in something like a man-o-war style colony. If this process proceeds long enough for all the creatures involved to be entirely co-dependant then it may be classified as one creature, despite being made from several.
This creature could be either ocean going or land-bound (my personal favourite environ for it would be a tidal estuary) and would be mostly sessile. It's also worth noting that the 'intelligence' would be distinctly different from ours, but no less valid.
In this creature there are many organisms, some of which prevent predation, some of which are responsible for luring/ensnaring prey, and some of which (the most interesting ones) exchange biochemical signals with each other and the other organisms in such a way that they can solve complex problems/ be aware that they are a thing. Imagine an ant colony, but with the ants being microscopic, numbering in the billions and having had some serious pressure to evolve more complex problem solving mechanisms.
This organisation would have a distinctly different structure to a human brain, potentially manifesting as a constantly shifting sense of self, no discernible personality, or very short term memory when not actively working to resolve a problem. It's possible that this creature would have no interest in putting a jigsaw puzzle together if you asked it to, but would solve a 12x12 Rubik's cube to get some food from the middle of it. It would also have some serious processing lag. While it might be able to reconfigure to solve hideously complex problems, the signal delay between individual cells not bound into a structure like our brains are would approach situations in a dreamlike fashion. Don't expect fast reflexes.
This creature would have no 'heart', no 'brain' and no 'hands'. Some organisms might be responsible for nutrient transfer, but if it's similar to a man-o-war there would be no distinct resource transfer network, just an organisation of specialised cells that can be re-organised by the emergent intelligence as best required. Some organisms work together to solve problems and keep every other organism (and themselves) alive, but loss of a section of them will be patched up by the others (though it might cause confusion). Some organisms might be great at organising into temporarily strong structures for object manipulation, but without guidance from the 'brain' cells they'd just form a lichen-like blob.
It would be extremely weird to watch this beast doing anything. Imagine this thing trying to use a can opener on a tin of spaghetti. It would pull the can and the opener into itself, take a few seconds experimenting, then open the can inside itself before drawing the spaghetti and sauce out into a slowly diffusing mass of nutrients. Movement would be less of an active 'I am going here now' and more of a gradual relocation, like watching a banana tree move, or tracking a city over the course of millennia.
TL:DR: Beached man-o war/Uber-ant colony. No heart as it's distributed, intelligent because it's got complex emergent behaviour, and can eat/drink/breath/manipulate, just really weirdly.